Class Of Groups Research Articles

Book Reviews

Australian Journal of Politics & HistoryVolume 7, Issue 1 p. 125-146 Book Reviews First published: May 1961 https://doi.org/10.1111/j.1467-8497.1961.tb01023.xRead the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Book reviewed in this article: EUROPEAN VISION AND THE SOUTH PACIFIC 1768–1850: A Study in the History of Art and Ideas. By Bernar Smith. MARX, ENGELS AND THE POLITICS OF THE PEASANTRY. By Henry Mayer. THE UNITED STATES IN THE WORLD ARENA: An Essay in recent History. By W. W. Rostow. AMERICAN FOREIGN POLICY IN THE NUCLEAR AGE: Principles, Problems, and Prospects. By Cecil V. Crabb, Jr. CANADIANS AND FOREIGN POLICY; The Record of an Independent Investigation. By Fred Alexander. BUGANDA AND BRITISH OVERRULE 1900–1955: Two Studies. By D. Anthony Low and R. Cranford Pratt THE CHINESE IN NEW ZEALAND: A Study in Assimilation. By Ng Bickleen Fong. IMMIGRANTS IN AUSTRALIA: A Demographic Survey Based upon the 1954 Census. By Jerzy Zubrzycki, assisted by Nancy Kuskie. IMMIGRANTS IN AUSTRALIA STATISTICAL SUPPLEMENT. By J. Zubrzycki FEDERAL JURISDICTION IN AUSTRALIA. By Zelman Cowen. THE GOVERNMENT OF THE AUSTRALIAN STATES. Edited by S. R. Davis. AUSTRALIA'S WESTERN THIRD: A History of Western Australia from the first settlements to modern times. By F. K. Crowley. THE AUSTRALIAN LABOR MOVEMENT 1850–1907. Extracts from contemporary documents selected by R. N. Ebbels, with additions by members of the Noel Ebbels Memorial Committee. Edited, with an Introduction, by L. G. Churchward. RADICAL AND WORKING CLASS POLITICS: A Study of Eastern Australia, 1850–1910. By Robin Gollan. THE DEBTOR'S WAR: Scottish Capitalists and the Economic Crisis in Australia 1841–1846. By David S. Macmillan. UNWILLING EMIGRANTS: A Study of the Convict Period in Western Australia. By Alexandra Hasluck. Volume7, Issue1May 1961Pages 125-146 RelatedInformation

K-Radical classes and product radical classes of MV-algebras

Abstract For an MV-algebra let J 0() be the system of all closed ideals of ; this system is partially ordered by the set-theoretical inclusion. A radical class X of MV-algebras will be called a K-radical class iff, whenever ∈ X and is an MV-algebra with J 0() ≅ J 0(), then ∈ X. An analogous notation for lattice ordered groups was introduced and studied by Conrad. In the present paper we show that there is a one-to-one correspondence between K-radical classes of MV-algebras and K-radical classes of abelian lattice ordered groups. We also prove an analogous result for product radical classes of MV-algebras; product radical classes of lattice ordered groups were studied by Ton.

Ideal chains in radical theory

It is shown that in a well known characterization of radical classes, closure under unions of chains of ideals can be replaced by closure under unions of continuous well-ordered chains of ideals. Some consequences are discussed.

Selections of lattice-ordered Groups

It is well known that the quasitorsion class of archimedean \(\ell\)-groups is the class of \(\ell\)-groups G such that every closed convex \(\ell\)-subgroup is a polar, and it is also well known that the class of \(\ell\)-groups G such that every convex \(\ell\)-subgroup is a polar is a torsion class. By defining a selection on \(\ell\)-groups, these two results are generalized to show, whenever \({\mathcal{S}}_{1}\) and \({\mathcal{S}}_{2}\) are selections on \(\ell\)-groups, the class of \(\ell\)-groups G such that \({\mathcal{S}}_{1}(G) = {\mathcal{S}}_{2}(G)\) is a radical class. Three selections in particular — all convex \(\ell\)-subgroups, all polars, and all closed convex \(\ell\)-subgroups — and the radical classes determined by them are studied in some detail.

On radicals of module coalgebras

We introduce the notion of an idempotent radical class of module coalgebras over a bialgebra B . We prove that if R is an idempotent radical class of B -module coalgebras, then every B -module coalgebra contains a unique maximal B -submodule coalgebra in R . Moreover, a B -module coalgebra C is a member of R if, and only if, D B is in R for every simple subcoalgebra D of C . The collection of B -cocleft coalgebras and the collection of H -projective module coalgebras over a Hopf algebra H are idempotent radical classes. As applications, we use these idempotent radical classes to give another proofs for a projectivity theorem and a normal basis theorem of Schneider without assuming a bijective antipode.

On Jacobson Near-rings and Special Radicals

In this paper, we construct special radicals using class pairs of near-rings. We establish necessary conditions for a class pair to be a special radical class. We then define Jacobson-type near-rings and show that in most cases the class of all near-rings of this type is a special radical class. Subsequently, we investigate the relationship between each Jacobson-type near-ring and the corresponding matrix near-ring.

Radicals of 0-regular algebras

We consider a generalisation of the Kurosh--Amitsur radical theory for rings (and more generally multi-operator groups) which applies to 0-regular varieties in which all operations preserve 0. We obtain results for subvarieties, quasivarieties and element-wise equationally defined classes. A number of examples of radical and semisimple classes in particular varieties are given, including hoops, loops and similar structures. In the first section, we introduce 0-normal varieties (0-regular varieties in which all operations preserve 0), and show that a key isomorphism theorem holds in a 0-normal variety if it is subtractive, a property more general than congruence permutability. We then define our notion of a radical class in the second section. A number of basic results and characterisations of radical and semisimple classes are then obtained, largely based on the more general categorical framework of L. M\'arki, R. Mlitz and R. Wiegandt as in [13]. We consider the subtractive case separately. In the third section, we obtain results concerning subvarieties and quasivarieties based on the results of the previous section, and also generalise to subtractive varieties some results for multi-operator group radicals defined by simple equational rules. Several examples of radical and semisimple classes are given for a range of fairly natural 0-normal varieties of algebras, most of which are subtractive.

2-Azaadamantane N-Oxyl (AZADO) and 1-Me-AZADO: Highly Efficient Organocatalysts for Oxidation of Alcohols

Development of a stable nitroxyl radical class of catalysts, 2-azaadamantane N-oxyl (AZADO) and 1-Me-AZADO, for highly efficient oxidation of alcohols is described. AZADO and 1-Me-AZADO exhibit superior catalytic proficiency to TEMPO, converting various sterically hindered alcohols to the corresponding carbonyl compounds in excellent yields.

The Jacobson semiradical over a certain semiring

The concept of the semiradical class of semirings was introduced in [3]. The purpose of this paper is to study one such semiradicals, the Jacobson semiradicals, over certain semirings. We generalize the concept of the Jacobson radical of a ring to a semiring. Some properties of the Jacobson semiradical $ JS(R) $ of the semiring $R$ parallel those of ring theory. In Section 1 we describe some preliminary definitions. In Section 2 we define regular strongly austere semimodulse. Theorem 1 characterizes a regular strongly austere semimodule in terms of a regular modular maximal subtractive left ideal. We define $JS(R)$ and derive some properties of this structure. In Section 3 we show that the $ JS(R) $ of a semiring has many representations as the intersection of left ideals. One of the more important of these is that $ JS(R) $ is the intersection of all left weakly primitive subtractive ideals. Proposition 6 characterizes a semiweekly primitive semiring in terms of a weakly primitive semiring. The interrelationships of strongly austere, weakly primitive and semiweekly primitive semirings are examined in Theorem 3. In Section 4, Proposition 7 shows that the $ JS(R) $ of a semiring with identity is the intersection of all regular maximal modular subtractive left ideals. Corollary 3 shows that $ JS(R) $ is the unique largest superfluous left ideal of $ R $. Proposition 8 shows that the class of Jacobson semiradical of semirings is closed under direct sum. We conclude with Section 5, a consideration of a certain restricted class of semirings. We show that the Jacobson semiradical for the semirings belonging to this class constitutes a semiradical class. Finally, Example 1 shows that a semiradical class need not be a radical class.

Radical and Torsion Theory for Acts

After recapitulating the rudiments of the Kurosh-Amitsur radical theory of S-acts, hereditary radicals are discussed. The hereditary Hoehnke radical assignments r which designate a Rees congruence r(A) to each S-act A, are the hereditary Kurosh-Amitsur radical assignments. Then the corresponding radical as well as semisimple classes are characterized. Equivalence classes of injective S-acts determine hereditary torsion assignments t, these are just the hereditary Hoehnke radicals, but the congruence t(A) of A need not be a Rees congruence. Torsion and torsionfree classes are characterized; several hereditary torsion assignments may determine the same torsion class which is always a radical class closed under taking subacts. Examples show that a hereditary torsion assignment need not be a hereditary radical.

Variation in tree growth, mortality and recruitment among topographic positions in a warm temperate forest

Questions: Do the population dynamics of trees differ among topographic positions and, if so, how does topographic position affect the population dynamics of species that are distributed in a topography-specific manner? Which is the most important life stage in determining vegetation patterns? Location: Primary and secondary warm temperate evergreen broad-leaved forest (40 - 280 m a.s.l.) on the western part of Yakushima Island, Japan. Methods: Mortality, recruitment, DBH growth and distribution of stems (≥ 5 cm DBH) in a 2.62-ha plot were surveyed in 1992 and 2002 to determine the relationships between population parameters and (1) topography and (2) distribution patterns of 17 common tree species. Results: Common species (n = 17) were classified into three distribution pattern groups: group A, distributed mainly on convex slopes; group B, on concave slopes, and group C, not aggregated with respect to topographic position. Stem mortality, recruitment and DBH growth were greater in group A than in group B within each topographic class. The hierarchy of stem mortality among topographic classes for groups A and B was convex > planar > concave. Stem recruitment density was relatively high on the convex and concave slopes, respectively, for groups A and B. Conclusions: The topographical positions of adult trees were not always most suited for adult survival and growth. For group A, the distribution pattern of adults was determined in the juvenile stage, while this was not the case for group B. Studies of juvenile stages are important for understanding the demographic basis of vegetation distribution patterns.

Essential extensions and radical classes of lattice-ordered groups

In this paper the relationship between essential extensions and radical classes of lattice-ordered groups is discussed. It is proved that the polar radical classes of lattice-ordered groups are exactly essentially closed classes.

Near-Ring Radicals and Class Pairs

For near-ring ideal mappings ρ1and ρ2, we investigate radical theoretical properties of and the relationship among the class pairs (ρ1: ρ2), [Formula: see text] and (ℛρ2: ℛρ1). Conditions on ρ1and ρ2are given for a general class pair to form a radical class of various types. These types include the Plotkin and KA-radical varieties. A number of examples are shown to motivate the suitability of the theory of Hoehnke-radicals over KA-radicals when radical pairs of near-rings are studied. In particular, it is shown that [Formula: see text] forms a KA-radical class, where [Formula: see text] denotes the class of completely prime near-rings and [Formula: see text] the class of 3-prime near-rings. This gives another near-ring generalization of the 2-primal ring concept. The theory of radical pairs are also used to show that in general the class of 3-semiprime near-rings is not the semisimple class of the 3-prime radical.

Indirect British Rule, State Formation, and Welfarism in Kerala, India, 1860–1957

This article examines the relationship between a strong nineteenth-century welfarist expansion between the 1860s and early 1940s, in Kerala, India, under indirect British rule, and the “exceptional” antipoverty regime that democratically elected Communists implemented during the postcolonial (post 1947) era in the state. While much attention has focused on Kerala as a model of social development and on postindependence state policies in creating it, no single work has attempted to understand the significance of its prior legacy of welfare. This article uses methods of comparative historical sociology to trace the historical making of Kerala's “exceptionalism.” It argues that the early welfare policies in Kerala were implemented in a dependent colonial context and aimed at warding off annexation by the British, but their unintended consequences were to stimulate what they were precisely designed to avoid—radical caste and class movements. The analysis suggests that the form and content of welfare policies are shaped by the exigencies of state formation, as state autonomy theorists would argue; however, it shows that political struggles are the decisive determining factors of the former.

Weak radical classes

We introduce the concept of weak radical classes and proceed to construct these classes. In section 2 we define strongly austere semimodules. Theorem 1 characterizes strongly autere semimodules with respect to modular maximal subtractive ideals. We present an example of a weak radical class that can be neither a semiradical class nor a radical class. In section 4 we show that the semiradical class over a certain restricted class of semirings is equivalent to the weak radical class. We also demonstrate the construction of a semiradical class over this class. Finally, we show in example 3 that a semiradical class need not to be a radical class.

On Some Interpolation Rules for Lattice Ordered Groups

Let α be an infinite cardinal. In this paper we define an interpolation rule IR(α) for lattice ordered groups. We denote by C(α) the class of all lattice ordered groups satisfying IR(α), and prove that C(α) is a radical class.

Archimedean Closed Lattice-Ordered Groups

We show that, if an abelian lattice-ordered group is archimedean closed, then each principal l-ideal is also archimedean closed. This has given a positive answer to the question raised in 1965 and hence proved that the class of abelian archimedean closed lattice-ordered groups is a radical class. We also provide some conditions for latticeordered group F (∆, R) to be the unique archimedean closure of ∑ (∆, R). Introduction. Throughout, let G be a lattice-ordered group (lgroup). Let Γ be a root system, that is, Γ is a partially ordered set for which {α ∈ Γ | α ≥ γ} is totally ordered, for any γ ∈ Γ. Let {Hγ | γ ∈ Γ} be a collection of abelian totally-ordered groups indexed by Γ. V (Γ, Hγ) is the set of all functions v on Γ for which v(γ) ∈ Hγ and the support of each v satisfies ascending chain condition. V (Γ, Hγ) is an abelian group under addition. Furthermore, if we define an element of V (Γ, Hγ) to be positive, if it is positive at each maximal element of its support, then V (Γ, Hγ) is an abelian l-group, which we call a Hahn group on Γ. ∑ (Γ, Hγ) is the l-subgroup of V (Γ, Hγ) whose elements have finite supports. A root in a root system Γ is a totally ordered subset of Γ. F (Γ, Hγ) is the l-subgroup of V (Γ, Hγ) such that the support of each element is contained in a finite number of roots in Γ. A convex l-subgroup which is maximal with respect to not containing some g ∈ G is called regular and is a value of g. Element g is special if it has a unique value, and in this case the value is called a special value. A convex l-subgroup P of G is prime if a∧b = 0 in G implies that either a ∈ P or b ∈ P . Regular subgroups of G are prime and form a root system under inclusion, written Γ(G). A subset ∆ ⊆ Γ(G) is plenary if ∩∆ = {0} and ∆ is a dual ideal in Γ(G); that is, if δ ∈ ∆, γ ∈ Γ(G) and γ > δ, then γ ∈ ∆. If G is an abelian l-group, then G is l-isomorphic to Received by the editors on September 8, 1998, and in revised form on May 31, 2001. Copyright c ©2004 Rocky Mountain Mathematics Consortium

On Polynomial and Multiplicative Radicals

We show that polynomial and multiplicative radicals in [1] are special cases of radicals defined by means of elements. We scrutinize the way of defining a radical γG by a subset G of polynomials in noncommuting indeterminates. Defining polynomial radicals, Drazin and Roberts [1] required that the set G be closed under composition of polynomials, and for multiplicative radicals two further conditions were demanded. We impose milder (in fact, necessary and sufficient) conditions, and call the so obtained radicals as weak polynomial and weak multiplicative radicals. The Baer (prime) radical is an example for a weak multiplicative (and so weak polynomial) radical which is not a polynomial (and so not a multiplicative) radical. The radical class of all rings A for which the polynomial ring A[x] is a Brown-McCoy radical ring (see [3]) is characterized in terms of commutators, and is shown to be a multiplicative radical.

A detailed investigation of subsitituent effects on N-h bond enthalpies in aniline derivatives and on the stability of corresponding N-centered radicals.

The N-H bond dissociation enthalpies (BDE's) of 40 anilines (pGC(6)H(4)NHY) from series 1 to 4 with alpha-Y and p-G substituents and the stability of related radicals (pGC(6)H(4)Ndot;Y) were studied using ab initio (MP2) and density functional methods (B3LYP) with large basis sets. The results show that both methods reproduce earlier experimental BDEs within 2-3 kcal/mol and satisfactorily predict the alpha and remote substituent effects on BDEs (DeltaBDEs), as they reproduced the experimental DeltaBDEs within less than 1 kcal/mol. Furthermore, the conventional radical stabilization enthalpy (RSE = - DeltaBDE) was found to be invalid to represent the trend of the radical stabilization because the molecule effect (ME) can contribute more to RSE than the radical effect (RE) for certain series (1 and 4). These radicals are in fact stabilized by electron-withdrawing groups (EWGs) but destabilized by electron-donating groups (EDGs), a phenomenon just opposite to the observed O-behavior of many other aromatic heteroatomic radicals studied so far. These radicals are thus assigned as a new radical class, Class counter-O (or O) according to Walter's terminology. Moreover, the excellent multi-parametric Hammett-type correlations indicated that the para substituent effects on BDEs originate mainly from polar effects, but those on radical stability originate from both spin delocalization and polar effects. The atomic charge and spin population variations at a radical center due to p-G substitution were also found to correlate satisfactorily with REs. These results show that the spin delocalization effect should be explicitly considered in accounting for both DeltaBDEs and radical stabilization effects. Finally, an overall subsituent effect scale for radical stability has been proposed, and the overall substituent effect on the N-radicals was found to conform to the Capto-dative Principle.

Torsion classes of MV-algebras

Torsion classes of MV-algebras are defined as radical classes which are closed with respect to homomorphisms; in this paper we investigate their relations to radical classes of lattice ordered groups and to varieties of MV-algebras.