Class Of Rings Research Articles

On Bass Modules and Semi-V-Modules

Let R be a commutative ring with identity. An $R$-module $M$ is called a semi-V-module if every nonzero homomorphic image of $M$ contains a nonzero V-submodule. An $R$-module $M$ is called a Bass module if every nonzero module in $\sigma [M]$ has a maximal submodule. It is shown that an $R$-module $M$ is a semi-V-module if and only if every nonzero cyclic submodule of $M$ is a Bass module if and only if $R/Ann_R(x)$ is a Bass ring for every nonzero element $x \in M$. Among other results, we characterize the class of rings $R$ for which every semi-V-module is a V-module and the class of rings $R$ for which every semi-V-module is a semisimple module. Also, we characterize the rings $R$ for which the class of semi-V-modules (Bass modules) is closed under direct products.

Centrally Essential Group Algebras and Classical Rings of Fractions

Centrally Essential Group Algebras and Classical Rings of Fractions

Contramodules over pro-perfect topological rings

Abstract For four wide classes of topological rings R \mathfrak{R} , we show that all flat left R \mathfrak{R} -contramodules have projective covers if and only if all flat left R \mathfrak{R} -contramodules are projective if and only if all left R \mathfrak{R} -contramodules have projective covers if and only if all descending chains of cyclic discrete right R \mathfrak{R} -modules terminate if and only if all the discrete quotient rings of R \mathfrak{R} are left perfect. Three classes of topological rings for which this holds are the complete, separated topological associative rings with a base of neighborhoods of zero formed by open two-sided ideals such that either the ring is commutative, or it has a countable base of neighborhoods of zero, or it has only a finite number of semisimple discrete quotient rings. The fourth class consists of all the topological rings with a base of neighborhoods of zero formed by open right ideals which have a closed two-sided ideal with certain properties such that the quotient ring is a topological product of rings from the previous three classes. The key technique on which the proofs are based is the contramodule Nakayama lemma for topologically T-nilpotent ideals.

Invertibles in topological rings: a new approach

Every element in the boundary of the group of invertibles of a Banach algebra is a topological zero divisor. We extend this result to the scope of topological rings. In particular, we define a new class of semi-normed rings, called almost absolutely semi-normed rings, which strictly includes the class of absolutely semi-valued rings, and prove that every element in the boundary of the group of invertibles of a complete almost absolutely semi-normed ring is a topological zero divisor. To achieve all these, we have to previously entail an exhaustive study of topological divisors of zero in topological rings. In addition, it is also well known that the group of invertibles is open and the inversion map is continuous and \(\mathbb {C}\)-differentiable in a Banach algebra. We also extend these results to the setting of complete normed rings. Finally, this study allows us to generalize the point, continuous and residual spectra to the scope of Banach algebras.

Load testing and simulation of asymmetric cable-net used for flexible rockfall protection barriers

Flexible protection barriers are often located on the mountainsides in order to decrease the risk of rockfall. In the present study, different scales of experimental tests are considered, to gauge the behaviour and to estimate the bearing capacity of a new type of cable-nets used for these flexible barriers in case of quasi-static loads. A large experimental campaign addressing cables characterization, as well as the behaviour of the constitutive cells of the net, which particular shape, a water drop shape instead of the classical rings, induces asymmetric loading transfer. Finally, the net behaviour itself is characterized through appropriate tests. These tests highlighted the non-linear behaviour perceived at different scales and permitted to evaluate the bearing capacity of the various components. Numerical simulations using the finite element code Abaqus were also conducted for the different components, a group of constitutive cells with rigid or fuse clip or the whole net, to reproduce the behaviour observed experimentally.

Winograd surgery can be performed under partial digital block in patients with ingrown toenails

Winograd procedures performed under a partial digital block with a single needle to the surgical side instead of the entire toe were not evaluated. This study aimed to examine the clinical results of classic ring block and partial digital block performed during Winograd procedures in cases of ingrown toenails. A total of 210 patients underwent Winograd surgery were divided into two groups according to the type of anesthesia used as follows: traditional ring block (TRB) and partial digital block (PDB). Visual analog scale (VAS) scores, Heifetz stage patient satisfaction levels, recurrence rates, and need for reoperation were recorded. Compared with the PDB group, the during operation VAS score was statistically significantly higher in the TRB group (p=0001). There was no statistically significant difference between the groups in terms of postoperative satisfaction, recurrence (p=0294), and reoperation rates (p=0651). This study is the first to show that adequate anesthetic efficacy can be achieved with a less invasive intervention for Winograd procedures.

On existence of joins and meets under the star order in strong Rickart rings

A strong Rickart ring is a Rickart ring which has some special properties that make it similar, in some respects, to Rickart *-rings. It is known that the star partial order on a Rickart *-ring can be characterized by a condition not involving involution; this allows one to define the star order also on strong Rickart rings. In the paper, we reconsider several conditions, known in the literature, for existence of joins and meets in Rickart *-rings under the star order. Our main purpose is to transfer the conditions, even those involving involution, to strong Rickart rings and to show that they are valid also in this wider class of rings.

Injective semimodules-revisited

Injective modules play an important role in characterizing different classes of rings (e.g. Noetherian rings, semisimple rings). Some semirings have no nonzero injective semimodules (e.g. the semiring of non-negative integers). In this paper, we study some of the basic properties of the so-called e-injective semimodules introduced by the first author using a new notion of exact sequences of semimodules. We clarify the relationships between the injective semimodules, the [Formula: see text]-injective semimodule, and the [Formula: see text]-injective semimodules through several implications, examples and counter examples. Moreover, we show that every semimodule over an arbitrary semiring can be embedded in a [Formula: see text]-[Formula: see text]-injective semimodule.

On rings whose quasi-injective modules are injective or semisimple

Two obvious classes of quasi-injective modules are those of semisimples and injectives. In this paper, we study rings with no quasi-injective modules other than semisimples and injectives. We prove that such rings fall into three classes of rings, namely, (i) QI-rings, (ii) rings with no middle class, or (iii) rings that decompose into a direct product of a semisimple Artinian ring and a strongly prime ring. Thus, we restrict our attention to only strongly prime rings and consider hereditary Noetherian prime rings to shed some light on this mysterious case. In particular, we prove that among these rings, QIS-rings which are not of type (i) or (ii) above are precisely those hereditary Noetherian prime rings which are idealizer rings from non-simple QI-overrings.

Construction of anti-cyclotomic Euler systems of modular abelian varieties, and the ranks of their Mordell-Weil groups

We generalize Birch's construction of the Heegner points on X0(N) to construct new points X1(N) (and therefore construct points on the abelian varieties associated to J1(N)). Then, we show that these points form an Euler system, and we improve Kolyvagin's Euler system techniques to show that for our point PτK/c and any ring class character χ of the extended ring class field of conductor c satisfying χ=χ‾, if PτK/cχ is non-torsion and GK→AutAf[π] is surjective, then the corank of Sel(Aχ/K) is 1, which implies the rank of Af(K)χ is 1.

Quasi invo-clean rings

An element v of an arbitrary ring R is called aninvolution if v2= 1 and a quasi-involution if either v or 1−vis an involution. We thereby define R to be quasi invo-cleanas the one whose elements are written in the form ofa sum of an idempotent and a quasi-involution. This considerably extends the class of invo-clean rings introduced by the present author in Commun. Korean Math. Soc. (2017) and the class of weakly tripotent rings introducedby Breaz and Cˆımpean in Bull. Korean Math. Soc. (2018). We, more-over, prove the curious fact that the newly defined class of quasi invo-cleanrings actually coincides with the class of weakly invo-clean rings defined by Danchev in Afr. Mat. (2017).

Synthetic Strategies for the (+)-Grandisol, the Main Constituent of Boll Weevil Pheromone

This paper presents a short review of synthetic approaches aiming to synthesise (+)- Grandisol, the main constituent of grandlure, a pheromone mixture released by the boll weevil, which is proven to exhibit significant biological activity. (+)-Grandisol 1 is among the components of the male-produced pheromone of the boll weevil Anthonomuns grandis, an important pest of cotton crops in Mesoamerica (from the south USA to Argentina). As a result of its biological activity and unique structure, several synthetic approaches have been reported. The aim is to explore remarkable methodologies towards the synthesis of (+)-Grandisol 1. Several methodologies have been applied towards the synthesis of (+)-Grandisol 1, including classical methods for cyclobutane ring construction, which promoted substantial improvements to access this pheromone, as well as a better comprehension of its biological profile.

A family of constacyclic codes over a class of non-chain rings $${\mathcal {A}}_{q,r}$$ and new quantum codes

A family of constacyclic codes over a class of non-chain rings $${\mathcal {A}}_{q,r}$$ and new quantum codes

Characterizations of maximal z°-ideals of C(X) and real maximal ideals of q(X)

In this paper we first give elementwise characterizations of real maximal ideals and maximal z°-ideals of C(X). Next, using this we characterize the real maximal ideals of the classical ring of quotients q(X) of C(X) and also maximal z°-ideals of factor rings of C(X). We show that every real maximal ideal of q(X) is precisely the extension of a real maximal ideal of C(X) which is also a z° -ideal, i.e., the extension of Mp for some almost P -point p of υX. Using this fact it turns out that in contrast to C(X), q(X) may not contain any real maximal ideal. We observe that every maximal ideal of q(X) is real if and only if X is a pseudocompact almost P -space, i.e., q(X) = C*(X). We also observe that the real maximal ideals of q(X) are precisely the extensions of the real maximal ideals of C(X) when and only when X is an almost P -space, i.e., q(X) = C(X).

Quasi-clean rings and strongly quasi-clean rings

An element [Formula: see text] of a ring [Formula: see text] is called a quasi-idempotent if [Formula: see text] for some central unit [Formula: see text] of [Formula: see text], or equivalently, [Formula: see text], where [Formula: see text] is a central unit and [Formula: see text] is an idempotent of [Formula: see text]. A ring [Formula: see text] is called a quasi-Boolean ring if every element of [Formula: see text] is quasi-idempotent. A ring [Formula: see text] is called (strongly) quasi-clean if each of its elements is a sum of a quasi-idempotent and a unit (that commute). These rings are shown to be a natural generalization of the clean rings and strongly clean rings. An extensive study of (strongly) quasi-clean rings is conducted. The abundant examples of (strongly) quasi-clean rings state that the class of (strongly) quasi-clean rings is very larger than the class of (strongly) clean rings. We prove that an indecomposable commutative semilocal ring is quasi-clean if and only if it is local or [Formula: see text] has no image isomorphic to [Formula: see text]; For an indecomposable commutative semilocal ring [Formula: see text] with at least two maximal ideals, [Formula: see text]([Formula: see text]) is strongly quasi-clean if and only if [Formula: see text] is quasi-clean if and only if [Formula: see text], [Formula: see text] is a maximal ideal of [Formula: see text]. For a prime [Formula: see text] and a positive integer [Formula: see text], [Formula: see text] is strongly quasi-clean if and only if [Formula: see text]. Some open questions are also posed.

Comparative studies of IR spectra of deprotonated serine with classical and thermostated ring polymer molecular dynamics simulations.

Here we report the vibrational spectra of deprotonated serine calculated from the classical molecular dynamics (MD) simulations and thermostated ring-polymer molecular dynamics (TRPMD) simulation with third-order density-functional tight-binding. In our earlier study [Inakollu and Yu, “A systematic benchmarking of computational vibrational spectroscopy with DFTB3: Normal mode analysis and fast Fourier transform dipole autocorrelation function,” J. Comput. Chem. 39, 2067 (2018)] of deprotonated serine, we observed a significant difference in the vibrational spectra with the classical MD simulations compared to the infrared multiple photon dissociation spectra. It was postulated that this is due to neglecting the nuclear quantum effects (NQEs). In this work, NQEs are considered in spectral calculation using the TRPMD simulations. With the help of potential of mean force calculations, the conformational space of deprotonated serine is analyzed and used to understand the difference in the spectra of classical MD and TRPMD simulations at 298.15 and 100 K. The high-frequency vibrational bands in the spectra are characterized using Fourier transform localized vibrational mode (FT-νNAC) and interatomic distance histograms. At room temperature, the quantum effects are less significant, and the free energy profiles in the classical MD and the TRPMD simulations are very similar. However, the hydrogen bond between the hydroxyl–carboxyl bond is slightly stronger in TRPMD simulations. At 100 K, the quantum effects are more prominent, especially in the 2600–3600 cm−1, and the free energy profile slightly differs between the classical MD and TRPMD simulations. Using the FT-νNAC and the interatomic distance histograms, the high-frequency vibrational bands are discussed in detail.

Revisiting the Partial Ring Current Model: Longitudinal Asymmetry of Ground Magnetic Depression During Geomagnetic Storms

AbstractDuring the main phase of geomagnetic storms, the horizontal ground magnetic component is more depressed at dusk than at dawn, which was originally explained by the partial ring current model. Later studies questioned the idea that the ring current intensifies primarily at dusk, and the cause of this dawn‐dusk asymmetry still remains to be understood. The present study targets this old issue by statistically examining SuperMAG geomagnetic (sub‐)indices. The results are summarized as follows: (1) the dawn‐dusk asymmetry is correlated with the enhancement of the dawnside westward auroral electrojet (AEJ); (2) its correlation with the duskside eastward AEJ, which was considered by the classical partial ring current model, is insignificant; (3) the magnetic depression tends to be larger on the dayside than on the nightside, and the asymmetry is correlated with the westward AEJ in the midnight sector; (4) the dawn‐dusk asymmetry enhances typically for 1–2 h, and the day‐night asymmetry for <1 h; (5) the dawn‐dusk and day‐night asymmetries are not correlated with each other. It is suggested that the dawn‐dusk asymmetry is associated with a dawnside wedge current system with an enhanced westward AEJ (1 & 2), and it is suggested to be driven by a substorm‐like process, and possibly also by enhanced global convection (4). The day‐night asymmetry is probably associated with the formation of the substorm wedge current system (3 & 4). Although the associated dawnside and midnight westward AEJs may often enhance simultaneously, they are possibly driven by different processes (4 & 5).

An Innovative Method for Microcapsule Based Functional Yarn Production

ABSTRACT Today, microcapsule application to textile materials is a widely used for the production of functional textile products. Microcapsule application methods used in practice have some significant disadvantages. There is a need for innovative methods to eliminate or minimize these disadvantages. From this point of view, in this study, it was aimed to develop an alternative method based on integrating microcapsule particles into the open staple fiber bundle before the spun yarn formation on the classical ring spinning. It was thought that this application method could allow the incorporating microcapsules not only the fibers on the yarn surface but also to the surface of the fibers in the yarn structure. Microcapsule doped and undoped ring spun yarns having Ne 16 yarn count with knitted twist were produced from viscose fibers. Obtained ring spun yarns were subjected to winding and knitting processes in order to analyze the effect of friction on the microcapsule presence. SEM images taken from yarn and fabric samples were examined. Additionally, yarn properties were analyzed. In order to evaluate the performance of the alternative method, microcapsule dispersion at the same concentration was applied to the knitted fabrics using pad-dry-cure method, which was widely used for production of the functional textile products. Two types of microcapsule applied knitted fabric samples were washed several times and presence of microcapsules was evaluated with SEM images. Furthermore, thermal properties of the both types of application methods were compared by examining T-history curves. The findings indicated that the alternative method offers comparable yarn and thermal properties with environmentally friendly application as well as washable and durable to the friction effects occurring in industrial processes.

On strongly coseparable modules

A module M is called mathfrak {s}-coseparable if for every nonzero submodule U of M such that M/U is finitely generated, there exists a nonzero direct summand V of M such that V subseteq U and M/V is finitely generated. It is shown that every non-finitely generated free module is mathfrak {s}-coseparable but a finitely generated free module is not, in general, mathfrak {s}-coseparable. We prove that the class of mathfrak {s}-coseparable modules over a right noetherian ring is closed under finite direct sums. We show that the class of commutative rings R for which every cyclic R-module is mathfrak {s}-coseparable is exactly that of von Neumann regular rings. Some examples of modules M for which every direct summand of M is mathfrak {s}-coseparable are provided.

Semicommutative involution rings

In this paper, we establish a generalization of the class of semicommutative rings which is called * -semicommutative ring. We also discuss the relations among * -semicommutative rings, * -reversible rings and reversible rings. Moreover, we investigate some properties of these rings.