Endomorphism Rings Of Abelian Groups Research Articles

On a topology in endomorphism rings of abelian groups

On a topology in endomorphism rings of abelian groups

On limit operations in a certain topology for endomorphism rings of abelian groups

On limit operations in a certain topology for endomorphism rings of abelian groups

On transitivity-like properties for torsion-free Abelian groups

Abstract We study some close relationships between the classes of transitive, fully transitive and Krylov transitive torsion-free Abelian groups. In addition, as an application of the achieved assertions, we resolve some old-standing problems, posed by Krylov, Mikhalev and Tuganbaev in their monograph [P. A. Krylov, A. V. Mikhalev and A. A. Tuganbaev, Endomorphism Rings of Abelian Groups, Kluwer Academic, Dordrecht, 2003]. Specifically, we answer Problem 44 from there in the affirmative by constructing a Krylov transitive torsion-free Abelian group which is neither fully transitive nor transitive. This extends to the torsion-free case certain similar results in the p-torsion case. We, alternatively, also expand to the torsion-free version some of the results concerning transitivity, full transitivity and Krylov transitivity in the p-primary case.

The ring of stable homotopy classes of self-maps of [formula omitted]-polyhedra

We raise the problem of realisability of rings as {X,X} the ring of stable homotopy classes of self-maps of a space X. By focusing on An2-polyhedra, we show that the direct sum of three endomorphism rings of abelian groups, one of which must be free, is realisable as {X,X} modulo the acyclic maps. We also show that Fp3 is not realisable in the setting of finite type An2-polyhedra, for p any prime.

Centrally essential endomorphism rings of abelian groups

We study Abelian groups A with centrally essential endomorphism ring If A is a such group which is either a torsion group or a non-reduced group, then the ring is commutative. We give examples of Abelian torsion-free groups of finite rank with non-commutative centrally essential endomorphism rings.

On Some Properties of Endomorphism Rings of Abelian Groups

Some equivalent conditions under which a group can be (fully) transitive, endotransitive, or weakly transitive are presented.

On the endomorphism rings of abelian groups and their Jacobson radical

We give a characterization of those abelian groups which are direct sums of cyclic groups and the Jacobson radicals of their endomorphism rings are closed. A complete characterization of p-groups A for which \(({\textit{EndA}},\mathcal T_L)\) is locally compact, where \(\mathcal T_L\) is the Liebert topology on \({\textit{EndA}}\) is given. We prove that if A is a countable elementary p-group then \({\textit{EndA}}\) has a non-admissible ring topology. To every functorial topology on A a right bounded ring topology on \({\textit{EndA}}\) is attached. By using this topology we construct on \({\textit{EndA}}\) a non-metrizable and non-admissibe ring topology for elementary countable p-groups A.

On regular endomorphism rings of topological Abelian groups

We extend a result of Rangaswamy about regularity of endomorphism rings of Abelian groups to arbitrary topological Abelian groups. Regularity of discrete quasi-injective modules over compact rings modulo radical is proved. A characterization of torsion LCA groups A for which End c (A) is regular is given.

Admissible topologies on endomorphism rings

We study in this paper admissible topologies on the endomorphism rings of Abelian groups. Various examples of admissible (non-admissible) topologies are given.

Realization Theorems for Triangular Rings

Realization Theorems for Triangular RingsTriangular matrix rings which are endomorphism rings of Abelian groups are characterized and Abelian groups with (or without) triangular endomorphism rings are investigated.

Strict radicals and endomorphism rings

We consider the determination of ring radicals by classes of modules as first discussed by Andrunakievich and Ryabukhin, but in cases where the modules concerned are defined by additive properties. Such a radical is the upper radical defined by the class of subrings of a class of endomorphism rings of abelian groups and is therefore strict. Not every strict radical is of this type, and while the A-radicals are of this type, there are others, including some special radicals. These investigations bring radical theory into contact with (at least) two questions from other parts of algebra. Which rings are endomorphism rings? For a given ring R, which abelian groups are non-trivial R-modules?

Properties of Endomorphism Rings of Abelian Groups. II

Properties of Endomorphism Rings of Abelian Groups. II

Endomorphism rings of Abelian groups as isomorphic restrictions of full endomorphism rings. II

Endomorphism rings of Abelian groups as isomorphic restrictions of full endomorphism rings. II

Endomorphism rings of abelian groups as isomorphic restrictions of full endomorphism rings

Endomorphism rings of abelian groups as isomorphic restrictions of full endomorphism rings

Endomorphism rings of abelian groups

Endomorphism rings of abelian groups

Endomorphism Rings of Abelian Groups with Ample Divisible Subgroups

Endomorphism Rings of Abelian Groups with Ample Divisible Subgroups

Endomorphism rings of Abelian groups generated by automorphism groups

Endomorphism rings of Abelian groups generated by automorphism groups