Class Of Groups Research Articles

Lexico groups and related radical classes

Abstract There are defined and studied radical classes of lattice ordered groups, in some way related to the notion of lexico extensions. It is shown that such radical classes form a proper class and they fail to be torsion classes.

On a type of distributivity of lattice ordered groups

Abstract Let m be an infinite cardinal. Inspired by a result of Sikorski on m-representability of Boolean algebras, we introduce the notion of r m-distributive lattice ordered group. We prove that the collection of all such lattice ordered groups is a radical class. Using the mentioned notion, we define and investigate a homogeneity condition for lattice ordered groups.

On the Synthesis, Characterization and Reactivity of N‐Heteroaryl–Boryl Radicals, a New Radical Class Based on Five‐Membered Ring Ligands

The synthesis and physical characterization of a new class of N-heterocycle-boryl radicals is presented, based on five membered ring ligands with a N(sp(2) ) complexation site. These pyrazole-boranes and pyrazaboles exhibit a low bond dissociation energy (BDE; BH) and accordingly excellent hydrogen transfer properties. Most importantly, a high modulation of the BDE(BH) by the fine tuning of the N-heterocyclic ligand was obtained in this series and could be correlated with the spin density on the boron atom of the corresponding radical. The reactivity of the latter for small molecule chemistry has been studied through the determination of several reaction rate constants corresponding to addition to alkenes and alkynes, addition to O2 , oxidation by iodonium salts and halogen abstraction from alkyl halides. Two selected applications of N-heterocycle-boryl radicals are also proposed herein, for radical polymerization and for radical dehalogenation reactions.

On radical classes of hemirings

Based on the concept of accessible subhemirings and inspired by the work on the general Kurosh-Amitsur radical theory for rings, this paper studies the lower radical classes and the hereditary radical classes of hemirings. We characterize radical classes of hemirings, and construct a lower radical class from a homomorphically closed class. We provide a necessary and sufficient condition under which an upper radical class of hemirings becomes hereditary and prove that an upper radical class of a regular class of semirings is hereditary. Besides, we show that the Brown-McCoy radical class and a Jacobson-type radical class are hereditary.

Radical Classes Closed Under Products

Abstract This is a survey of what is known about Kurosh-Amitsur radical classes which are closed under direct products. Associative rings, groups, abelian groups, abelian ℓ-groups and modules are treated. We have attempted to account for all published results relevant to this topic. Many or most of these were not, as published, expressed in radical theoretic terms, but have consequences for radical theory which we point out. A fruitful source of results and examples is the notion of slenderness for abelian groups together with its several variants for other structures. We also present a few new results, including examples and a demonstration that e-varieties of regular rings are product closed radical classes of associative rings.

Embryonal Rhabdomyosarcoma of the Uterine Cervix in Adults

We report a case of cervical rhabdomyosarcoma in an adult and review of literature. A 44-year-old, premenopausal, white woman, complained of vaginal bleeding for 2 months. The gynecological examination showed a cervical polyp protruding from the vagina. The polyp was partially removed by polypectomy. Pathological examination was diagnostic for embryonal rhabdomyosarcoma-botryoid type-of the cervix. Radical class II hysterectomy, bilateral salpingo-oophorectomy, omentectomy, and pelvic lymphadenectomy were performed. Adjuvant multidrug chemotherapy (vincristine, doxorubicin, ifosfamide, and etoposide) plus external beam radiotherapy were administered. Forty-six months after diagnosis, the patient is disease free. Here, we report a new case and a literature review of a fairly rare cancer, rhabdomyosarcoma of the cervix in an adult. Pathological features and treatment with an aggressive multimodal approach (radical surgery followed by multidrug adjuvant chemotherapy and radiotherapy) are reported. Good treatment-tolerance and optimal results were achieved. Every effort should be done during both the diagnostic and therapeutic phase to offer these patients the best chance of survival. Further studies on best approach, chemotherapeutic protocols, and outcome in adults are warranted.

Politics of Indignation: Radical Democracy and Class Struggle beyond Postmodernity

This article analyzes the social impact, dynamics, and political organization of the Spanish revolt of the Indignados. The article starts with the emergence of the 15M in Spain, criticizing the representation of the movement in the media and exposing the political and economic conjuncture of Spain at the date of the revolt. Then it analyzes the Indignados sociopolitical phenomenon as an articulation of social movements linked by one method of political decision and association: the assembly. After this, it tries to explore the limits and advantages of a noninstitutionalized approach towards social conflict, exposing the social changes the movement has introduced into the Spanish society. Finally, it points out the real obstacles for the 15M as a post-Fordist class movement in an attempt to understand the role of the Indignados like an alternative for political change in Spanish society.

On radical classes of monounary algebras

On radical classes of monounary algebras

On base radical and semisimple classes defined by class operators

By using class operators, we define base radical and semisimple classes, within a broad abstract setting due to Puczylowski. The new notions agree with the usual Kurosh–Amitsur ones for associative rings and groups but differ for not necessarily associative rings, in general lying strictly between the Kurosh–Amitsur and torsion theory notions. A study of the class operators for their own sake is initiated, and a connection with modal logic is made.

Torsion classes of generalized Boolean algebras

Abstract Torsion classes and radical classes of lattice ordered groups have been investigated in several papers. The notions of torsion class and of radical class of generalized Boolean algebras are defined analogously. We denote by T g and R g the collections of all torsion classes or of all radical classes of generalized Boolean algebras, respectively. Both T g and R g are partially ordered by the class-theoretical inclusion. We deal with the relation between these partially ordered collection; as a consequence, we obtain that T g is a Brouwerian lattice. W. C. Holland proved that each variety of lattice ordered groups is a torsion class. We show that an analogous result is valid for generalized Boolean algebras.

Inordning och uppror

Fitting in and Rebelling: On the Ambivalence towards Tradition in Modern Swedish Working-Class Literature
 This article analyzes the ambivalent attitude of several Swedish working-class writers towards the tradition of working-class literature during the period 1945–2010. To certain extent, this ambivalence is a product of some aspects of the general symbolic economy in the field of literary production. Primarily, however, it is the result of conditions specific to Swedish working-class literature. Working-class writers often motivate their membership to the tradition of workingclass literature in terms of the tradition’s legitimizing of radical class discourses both within and beyond the field of literature. At the same time, however, the subaltern status of this tradition often makes its conventions for literary representations of class appear aesthetically and politically unsatisfactory. Furthermore, over time, the general cultural production of class on a societal level necessitates a break with the class-political literary strategies developed within the tradition of working-class literature.

GROUPS WITH CONTEXT-FREE CONJUGACY PROBLEMS

The conjugacy problem and the inverse conjugacy problem of a finitely generated group are defined, from a language theoretic point of view, as sets of pairs of words. An automaton might be obliged to read the two input words synchronously, or could have the option to read asynchronously. Hence each class of languages gives rise to four classes of groups; groups whose (inverse) conjugacy problem is an (a)synchronous language in the given class. For regular languages all these classes are identical with the class of finite groups. We show that the finitely generated groups with asynchronously context-free inverse conjugacy problem are precisely the virtually free groups. Moreover, the other three classes arising from context-free languages are shown all to coincide with the class of virtually cyclic groups, which is precisely the class of groups with synchronously one-counter (inverse) conjugacy problem. It is also proved that, for a δ-hyperbolic group and any λ ≥ 1, ϵ ≥ 0, the intersection of the inverse conjugacy problem with the set of pairs of (λ, ϵ)-quasigeodesics is context-free. Finally we show that the conjugacy problem of a virtually free group is an asynchronously indexed language.

Lie Dimension Subgroups and Central Series Related to Group Algebras

Let KG be the group algebra of a group G over a field K of positive characteristic p, and let 𝔇(n)(G) and 𝔇[n](G) denote the n-th upper Lie dimension subgroup and the n-th lower one, respectively. In [1] and [12], the equality 𝔇(n)(G) =𝔇[n](G) is verified when p ≥ 5. Motivated by [16, Problem 55], in the present paper we establish it for particular classes of groups when p ≤ 3. Finally, we introduce and study a new central series of G linked with the Lie nilpotency class of KG.

Polynomial Equation in Radicals

Necessary and sucient conditions for a radical class of rings to satisfy the polynomial equation (R(x)) = ( (R))(x) have been investigated. The interrelationship of polynomial equation, Amitsur property and polynomial extensibility is given. It has been shown that complete analogy of R.E. Propes result for radicals of matrix rings is not possible for polynomial rings.

A NOTE ON LOWER RADICALS OF HEMIRINGS

Abstract. In this paper, we generalize a few results of [7, 10] for lowerradical classes of rings, by using the limit ordinal construction for lowerradical classes of hemirings. 1. Introduction and preliminariesD. M. Olson and T. L. Jenksins [8] discussed general Radical Theory ofHemirings. The theory was further enriched by many authors (see [4, 12, 13]).The lower radicals were investigated by (see [5, 6, 9, 10, 11]) for radical classesof rings. Here we are interesting to generalize a several results of (see [3, 7,10]) in the frame work of hemiring which is quite different from ring theoreticalapproach discussed in (see [3, 7, 10]).A semiring ( R, + ,· ) is called a hemiring if(i) ‘+’ is commutative,(ii) there exists an element 0 ∈ R such that 0 is the identity of ( R, +) andthe zero element of ( R,· ), i.e., 0 r = r 0 = 0, ∀r ∈ R .If I is an semi-ideals of R , then we denote I ≤ R .Lower radical classes for hemirings can be constructed similar to the con-struction of lower radicals for rings (see [3, 5, 6, 9, 10,11]).First we include necessary preliminary, let

Radical classes and weak radical mappings of GMV-algebras

Abstract We use the concept of generalized MV-algebra (GMV-algebra, in short) in the sense of Galatos and Tsinakis; the main tool in their investigation was a truncation construction. The relations between radical classes of GMV-algebras and radical classes of lattice ordered groups are investigated in the present paper. Further, we apply the truncation construction for dealing with weak retract mappings of GMV-algebras.

Homomorphic images of Abelian groups

For some classes of Abelian groups, we answer the question of when a union of homomorphic images of a group is a subgroup of another group. In connection with this, the concept of a homomorphically stable group is introduced and properties of homomorphically stable groups from different classes of Abelian groups are studied.

T-radicals in the category of Abelian groups

This paper is devoted to the class of idempotent radicals defined by means of a tensor product. We describe their effect on Abelian groups. The structure of the lattice of all such radicals is determined. We characterize these radicals in terms of the closure properties of their radical classes.

On some types of radical classes

Let $$ \mathfrak{m} $$ be an infinite cardinal. We denote by $$ C_\mathfrak{m} $$ the collection of all $$ \mathfrak{m} $$ -representable Boolean algebras. Further, let $$ C_\mathfrak{m}^0 $$ be the collection of all generalized Boolean algebras B such that for each b ∈ B, the interval [0, b] of B belongs to $$ C_\mathfrak{m} $$ . In this paper we prove that $$ C_\mathfrak{m}^0 $$ is a radical class of generalized Boolean algebras. Further, we investigate some related questions concerning lattice ordered groups and generalized MV-algebras.

RADICALS WITH THE α-AMITSUR PROPERTY

A radical γ of rings is said to have the Amitsur property if for all rings A, γ(A[X]) = (γ(A[X]) ∩ A)[X]. Let Xα denote a set of indeterminates of cardinality α. We say that γ has the α-Amitsur property if for all rings A, γ(A[Xα]) = (γ(A[Xα]) ∩ A)[Xα]. We study properties of this type of radicals and show relationships with other known radicals for rings. A ring A is said to be an absolute γ-ring if A[x1,…, xn] ∈ γ, for any n ∈ ℕ. We show that A is an absolute 𝔾-ring for the Brown–McCoy radical 𝔾, if and only if A is in the radical class S determined by the unitary strongly prime rings. Moreover, A is an absolute nil ring if and only if A is an absolute J-ring, where J denotes the Jacobson radical.