Decomposable Groups Research Articles

Near-isomorphism for bounded completely decomposable groups

In recent work the authors introduced the notion of near-isomorphism for torsion-free abelian groups of infinite rank. In a natural way this concept extends the classical definition of near-isomorphism in the finite rank case. We prove some further properties of this notion and introduce the new concept of bounded near-isomorphism which is a stronger form of near-isomorphism. As an application we study bounded near-isomorphic bounded completely decomposable abelian groups (bcd-groups). It is shown that bcd-groups allow a theory that is very similar to the theory of almost completely decomposable groups with respect to bounded near-isomorphism.

Filial rings on direct sums and direct products of torsion-free abelian groups

A ring whose additive group coincides with an abelian group G is called a ring on G. An abelian group G is called a TI-group if every associative ring on G is filial. If every (associative) ring on an abelian group G is an SI-ring (a hamiltonian ring), then G is called an SI-group (an SI_H-group). In this article, TI-groups, SI_H-groups and SI-groups are described in the following classes of abelian groups: almost completely decomposable groups, separable torsionfree groups and non-measurable vector groups. Moreover, a complete description of non-reduced TI-groups, SI_H-groups and SI-groups is given. This allows us to only consider reduced groups when studying TI-groups.

On the Question of Definability of Homogeneously Decomposable Torsion-Free Abelian Groups by Their Homomorphism Groups and Endomorphism Rings

Let $$C$$ be an Abelian group. A class $$X$$ of Abelian groups is called a $$_CH $$ -class (a $$_CEH$$ -class) if, for any groups $$A$$ and $$B$$ in the class $$X$$ , the isomorphism of the groups $$\operatorname{Hom}(C,A)$$ and $$\operatorname{Hom}(C,B)$$ (the isomorphism of the endomorphism rings $$E(A)$$ and $$E(B)$$ and of the groups $$\operatorname{Hom}(C,A)$$ and $$\operatorname{Hom}(C,B)$$ ) implies the isomorphism of the groups $$A$$ and $$B$$ . In the paper, we study conditions that must be satisfied by a vector group $$C$$ for some class of homogeneously decomposable torsion-free Abelian groups to be a $$_CH$$ class (Theorem 1), and also, for some $$C$$ in the class of vector groups, for some class of homogeneously decomposable torsion-free Abelian groups to be a $$_CEH$$ -class (Theorem 2).

Completely Decomposable Quotient Divisible Abelian Groups with Isomorphic Endomorphism Semigroups

Let $$\Lambda$$ be a class of Abelian groups. A group $$A\in\Lambda$$ is said to be determined by its endomorphism semigroup $$E^\star(A)$$ in the class $$\Lambda$$ if every isomorphism $$E^\star(A)\cong E^\star(B)$$ , where $$B\in\Lambda$$ , implies the isomorphism $$A\cong B$$ . The paper describes those Abelian groups in the class $$\mathscr Q\mathscr D_{\mathrm{cd}}$$ of completely decomposable quotient divisible Abelian groups which are determined by their endomorphism semigroups in the class $$\mathscr Q\mathscr D_{\mathrm{cd}}$$ .

Decompositions of decidable abelian groups

We use computability-theoretic tools to measure the complexity of the process of direct decomposing an abelian group based on its symbolic presentation. More specifically, we compare degrees of decidable categoricity of abelian groups with degrees of categoricity of their natural direct summands. As a nontrivial and unexpected application of our methods, we show that every decidable copy of a nondivisible homogeneous completely decomposable group has an algorithm for linear independence.

The microbial community size, structure, and process rates along natural gradients of soil salinity

Over 840 M ha of arable land is affected by salinization, and the area is predicted to increase due to global change. Assessments of the status of the microbial community in saline soils have frequently been based on microbial biomass estimates, which might not accurately reflect microbial process rates in soil. Moreover, assessments of how the relative importance of major decomposer groups bacteria and fungi are affected by salinity remain inconclusive. In this study we set out to assess the soil microbial community size, structure and process rates along two salinity gradients. To distinguish between the direct effects of high salinity and indirect effects resulting from reduced soil organic matter (OM) concentrations in saline soils we also assessed the gradients following plant litter amendments to compensate for differences in OM content between soils and isolate the effect of salinity. The research aims were to (i) investigate the microbial biomass responses to salinity as estimated based on both PLFA concentrations and qPCR measurements and to compare these responses to those of respiration and microbial growth, (ii) compare the responses of bacteria and fungi to increased salinity and (iii) assess the responses of these microbial variables to the alleviation of OM scarcity expected in saline soils. Microbial biomass estimates generally were less negatively affected by salinity than bacterial growth and respiration, and were not correlated to rates of microbial growth or respiration rates. While bacterial growth was strongly inhibited by salinity, fungal growth was similar in soils of all salinities, indicating a higher fungal tolerance to salinity. OM additions increased process rates in saline soils and alleviated some of the negative impact of salinity on respiration and growth. In conclusion, this study demonstrates differential responses of saprotrophic fungi and bacteria to increasing salinity and that bacteria are directly impacted by soil salinity while fungi are responding to the indirect effect by salinity related to reduced plant C input.

Stronger effects of litter origin on the processing of conifer than broadleaf leaves: A test of home‐field advantage of stream litter breakdown

Abstract Ecological shifts that enhance the efficiency of resource acquisition by consumers can affect the fate of resource subsidies in recipient ecosystems. To date, findings have been mixed about whether plant litter breakdown by stream decomposers is faster in locations where the litter originates from (i.e. home region) compared with other locations (away region). This phenomenon, known as home‐field advantage (HFA), may be influenced by litter quality and particularly decomposer groups (shredders versus microbes), rather than being an inherent consequence of the breakdown of locally native litter. We studied the effects of HFA on litter breakdown and litter‐associated communities in streams within mid‐ to late‐successional forests. Two pairs of riparian broadleaf and one pair of conifer litter species with contrasting chemical quality were reciprocally incubated across two temperate regions (˜3,000 km apart). Species in each pair are congeneric and allopatric. The HFA was assessed using within‐pair litter comparisons in home and away regions. Coarse‐ and fine‐mesh litterbags were used to separate the contributions to litter breakdown by microbial decomposition and shredder feeding. Conifer litter species used in this study were more recalcitrant than broadleaf litter species. Consequently, there was a significant positive HFA for the microbial decomposition of conifer litter. In contrast, there was no HFA for either microbial or shredder‐mediated breakdown of broadleaf litter, which might have been overridden by catchment‐scale differences in biophysical variables affecting breakdown. The effects of HFA on shredder colonisation and feeding on broadleaf litter were more variable among streams. Numerically abundant shredder taxa tended to have higher rates of colonisation and consumption on higher‐quality litter than on low‐quality litter, irrespective of litter origin. Our results suggest that prior (evolutionary and/or contemporary) litter exposure could strongly influence the litter‐processing capacity of microbial decomposers, but not shredders, at the community level. In particular, microbial decomposers specialised in degrading conifer litter probably had lower resource‐use plasticity than those processing broadleaf litter. Inter‐stream differences in riparian vegetation and habitat conditions could influence the HFA through altering the litter exposure history of decomposer communities. Our findings highlight the importance of prior litter–microbe interactions in determining the rates of microbial decomposition of native and exotic litter species.

Constellation-Optimal Beamformers for Multiuser MISO Broadcast Visible Light Communications

In this paper, we design energy-efficient space constellations for multiuser multi-input single-output visible light communication broadcast systems with channel state information (CSI) at the receiver in the three scenarios: 1) with CSI at the transmitter (CSIT); 2) with statistical CSIT; and 3) without CSIT. By utilizing the cooperation of multiuser interference, optimal multidimensional additively uniquely decomposable constellation groups are designed to optimize the received worst case performance metrics of all users subject to two commonly used power constraints, i.e., average and peak optical power constraints. The resulting optimal designs are proved to be pulse amplitude modulated with an optimal beamformer, which can be efficiently attained by numerical search for Scenarios 1 and 2 and be given in a closed form for Scenario 3. One of the common significant advantages of these designs is the fast demodulation of the sum signal from a noisy received signal, since these optimal designs result in an equivalent ideal scalar AWGN channel. Comprehensive computer simulations demonstrate that our designs significantly outperform traditional zero-forcing, minimum mean square error, and time-division methods.

Diversity of fungi in harvested forests 10 years after logging and burning: Polypore assemblages on different woody substrates

The negative biodiversity effects of timber- and biofuel-oriented forestry practices can be alleviated by leaving retention trees and logging residues following clear-cut harvests and occasionally including prescribed burns. Such measures can potentially maintain substrates especially for dead-wood-associated species during young, post-harvest successional stages. However, the availability and temporal patterns of different types of dead wood substrates after cutting are largely unknown, yet these patterns may have a major influence on fungal diversity.We sampled dead wood and the associated polypore fungi - a key wood decomposer group - in a large-scale field experiment with 24 sites, before logging and 2, 4 and 10 years after logging (clear-cut with and without retention trees) and burning. We investigated all old natural dead wood, stumps, slash and retention trees on each site, totaling 98,136 dead wood items. The data include 22,150 records of 122 polypore species collected across all sampling years.Ten years after treatments, we found no differences in the number of species between unlogged and logged or burned and unburned treatment categories, but on the treated sites, the numbers were higher than before treatments. Furthermore, the composition of species assemblages differed as the substrate types available varied between treatments. All dead wood substrate types hosted diverse polypore assemblages. The highest numbers of species were found on slash and retention trees. Furthermore, the polypore assemblages differed between dead wood types. Burning increased the number of species on stumps and red-listed species seemed to increase on burned sites.Our results show that dead wood can host diverse polypore assemblages also in managed forests after timber harvests. However, the pre-requisite for maintaining fungal diversity appears to be that – in addition to sufficient amount of substrates - also qualitative variation in dead wood substrates is maintained, including stumps and slash.

Bacteria constrain the fungal growth response to drying-rewetting

Bacteria and fungi are the two principal decomposer groups in soils, determining rates of biogeochemical cycling. Rewetting of dry soils induces enormous dynamics in biogeochemistry. Bacteria have been shown to exhibit large variation in growth over time upon drying-rewetting (D/RW), however, in studies to date, fungal growth has shown limited responsiveness. Here we investigated whether fungal growth responses to D/RW are constrained by competition with bacteria by using the bactericide bronopol to suppress bacterial growth during D/RW. We examined responses for two different soils, previously shown to exhibit different bacterial growth responses to D/RW. Experimental elimination of bacterial growth lead to increased fungal growth in both soils upon D/RW, indicating a competitive release of fungal growth when bacteria were suppressed. We also observed a pronounced fungal growth response to D/RW for one of the soils, which has not been previously reported. In this case, even when rewetting with water (i.e. without bacterial suppression), fungal growth increased to reach rates 10-times greater than in the moist control soil. The peak in fungal growth coincided with a secondary peak of respiration, revealing a functional importance of fungi for C-cycling during D/RW. The decline in fungal growth following this peak also coincided with the onset of exponential bacterial growth, further strengthening evidence for a negative correlation between bacteria and fungi, suggesting that competition with bacteria can constrain the fungal growth response to D/RW.

Definability of Completely Decomposable Torsion-Free Abelian Groups by Endomorphism Semigroups and Homomorphism Groups

Let C be an Abelian group. A class X of Abelian groups is called a CE•H-class if, for every groups A, B ∈ X, the isomorphisms E•(A) ≅ E•(B) and Hom(C, A) ≅ Hom(C, B) imply the isomorphism A ≅ B. In the paper, necessary and sufficient conditions on a completely decomposable torsion-free Abelian group C are described under which a given class of torsion-free Abelian groupsisa CE•H-class.

Microbial growth and carbon use efficiency in soil: Links to fungal-bacterial dominance, SOC-quality and stoichiometry

Microbial decomposers are responsible for the breakdown of organic matter (OM) and thus regulate soil carbon (C) stocks. During the decomposition of OM, microorganisms can use the assimilated C for biomass production or respire it as CO2, and the fraction of growth to total assimilation defines the microbial carbon-use efficiency (CUE). As such, CUE has direct consequences for how microbial decomposers affect the balance of C between atmosphere and soil. We estimated fungal and bacterial growth in C units in microcosm systems with submerged plant litter. We established conversion factors between bacterial and fungal growth to biomass and applied this to a dataset representing 9 different sites in temperate forest soils, temperate agricultural soils, and subarctic forest soils, to estimate growth rates of fungi and bacteria in units of C, to estimate the dominance of the two decomposer groups, and to compare these values to respiration to estimate the microbial CUE. We observed that fungal-to-bacterial growth ratios (F:B) ranged from 0.02 to 0.44, and that the fungal dominance was higher in soils with lower C:N ratio and higher C-quality. We found a negative exponential relationship between the dominance of fungi and the microbial CUE. CUE ranged from 0.03 to 0.30, and values clustered most strongly according to site rather than level of soil N. CUE was higher in soil with high C:N ratio and high C-quality. However, within each land-use type, a high mineral N-content did result in lower F:B and higher resulting CUE. In conclusion, a higher soil C-quality coincided with lower F:B and higher CUE across the surveyed sites, while a higher N availability did not. A higher N availability resulted in higher CUE and lower F:B within each site suggesting that site-specific differences such as the effect of plant community via e.g. plant litter and rhizosphere input, overrode the influence of N-availability.

Fungi participate in driving home-field advantage of litter decomposition in a subtropical forest

Home-field advantage (HFA) hypothesis predicts that plant litter decomposes faster beneath the plant species from which it was derived than beneath other plant species. However, it remains unclear, which groups of soil organisms drive HFA effects across a wide range of litter quality and forest types. We set up a reciprocal transplant decomposition experiment to quantify the HFA effects of broadleaf, coniferous and bamboo litters. Litterbags of different mesh sizes and high-throughput pyrosequencing of microbial rRNA gene were used to test the contribution of different decomposer groups to HFA effect. The recalcitrant broadleaf litter and the labile bamboo litter exhibited HFA. Presence of meso-and macrofauna did not substantially change the HFA effects. Bacterial and fungal community composition on litters were significantly influenced by litter type. Bacterial community composition remained unchanged when the same litter was decomposed in different forest types, whereas fungal community composition on broadleaf and bamboo litters were significantly influenced by incubation site. Our data demonstrate specific association between fungal community composition and faster litter decomposition in the home site, suggesting that fungi probably participate in driving the HFA effect of broadleaf and bamboo litters.

A Note on the Square Subgroups of Decomposable Torsion-Free Abelian Groups of Rank Three

AbstractA hypothesis stated in [16] is confirmed for the case of associative rings. The answers to some questions posed in the mentioned paper are also given. The square subgroup of a completely decomposable torsion-free abelian group is described (in both cases of associative and general rings). It is shown that for any such a group A, the quotient group modulo the square subgroup of A is a nil-group. Some results listed in [16] are generalized and corrected. Moreover, it is proved that for a given abelian group A, the square subgroup of A considered in the class of associative rings, is a characteristic subgroup of A.

Uncovering trophic positions and food resources of soil animals using bulk natural stable isotope composition.

Despite the major importance of soil biota in nutrient and energy fluxes, interactions in soil food webs are poorly understood. Here we provide an overview of recent advances in uncovering the trophic structure of soil food webs using natural variations in stable isotope ratios. We discuss approaches of application, normalization and interpretation of stable isotope ratios along with methodological pitfalls. Analysis of published data from temperate forest ecosystems is used to outline emerging concepts and perspectives in soil food web research. In contrast to aboveground and aquatic food webs, trophic fractionation at the basal level of detrital food webs is large for carbon and small for nitrogen stable isotopes. Virtually all soil animals are enriched in 13 C as compared to plant litter. This 'detrital shift' likely reflects preferential uptake of 13 C-enriched microbial biomass and underlines the importance of microorganisms, in contrast to dead plant material, as a major food resource for the soil animal community. Soil organic matter is enriched in 15 N and 13 C relative to leaf litter. Decomposers inhabiting mineral soil layers therefore might be enriched in 15 N resulting in overlap in isotope ratios between soil-dwelling detritivores and litter-dwelling predators. By contrast, 13 C content varies little between detritivores in upper litter and in mineral soil, suggesting that they rely on similar basal resources, i.e. little decomposed organic matter. Comparing vertical isotope gradients in animals and in basal resources can be a valuable tool to assess trophic interactions and dynamics of organic matter in soil. As indicated by stable isotope composition, direct feeding on living plant material as well as on mycorrhizal fungi is likely rare among soil invertebrates. Plant carbon is taken up predominantly by saprotrophic microorganisms and channelled to higher trophic levels of the soil food web. However, feeding on photoautotrophic microorganisms and non-vascular plants may play an important role in fuelling soil food webs. The trophic niche of most high-rank animal taxa spans at least two trophic levels, implying the use of a wide range of resources. Therefore, to identify trophic species and links in food webs, low-rank taxonomic identification is required. Despite overlap in feeding strategies, stable isotope composition of the high-rank taxonomic groups reflects differences in trophic level and in the use of basal resources. Different taxonomic groups of predators and decomposers are likely linked to different pools of organic matter in soil, suggesting different functional roles and indicating that trophic niches in soil animal communities are phylogenetically structured. During last two decades studies using stable isotope analysis have elucidated the trophic structure of soil communities, clarified basal food resources of the soil food web and revealed links between above- and belowground ecosystem compartments. Extending the use of stable isotope analysis to a wider range of soil-dwelling organisms, including microfauna, and a larger array of ecosystems provides the perspective of a comprehensive understanding of the structure and functioning of soil food webs.

Boundedness control sets for linear systems on Lie groups

Abstract Let Σ be a linear system on a connected Lie group G and assume that the reachable set 𝓐 from the identity element e ∈ G is open. In this paper, we give an algebraic condition to warrant the boundedness of the existent control set with a nonempty interior containing e. We concentrate the search for the class of decomposable groups which includes any solvable group and also every compact semisimple group.

On Abelian Groups with Commutative Commutators of Endomorphisms

Abelian groups with commutative commutators of endomorphisms are studied. The structure of these groups is described among torsion, completely decomposable, coperiodic, and split mixed groups.

On Determinability of a Completely Decomposable Torsion-Free Abelian Group by its Automorphism Group

In this paper, we consider the question of determinability of an Abelian group by its automorphism group in the class of completely decomposable torsion-free Abelian groups whose direct summands of rank 1 have idempotent types.

On Some Classes of Hopfian Abelian Groups and Modules

The hopficity property in a well-known class of Abelian groups—completely decomposable torsion-free groups—as well as in a class of modules over generalized matrix rings is studied. Examples of non-Hopfian completely decomposable torsion-free group are constructed.

FINITE TRIFACTORISED GROUPS AND -DECOMPOSABILITY

We derive some structural properties of a trifactorised finite group $G=AB=AC=BC$, where $A$, $B$, and $C$ are subgroups of $G$, provided that $A=A_{\unicode[STIX]{x1D70B}}\times A_{\unicode[STIX]{x1D70B}^{\prime }}$ and $B=B_{\unicode[STIX]{x1D70B}}\times B_{\unicode[STIX]{x1D70B}^{\prime }}$ are $\unicode[STIX]{x1D70B}$-decomposable groups, for a set of primes $\unicode[STIX]{x1D70B}$.