Endomorphism rings of Abelian groups

DOI10.1023/A:1015190932351zbMath1017.20047OpenAlexW4254873293MaRDI QIDQ5915518

Piotr A. Krylov, Alexander V. Mikhalev, Askar A. Tuganbaev

Publication date: 28 October 2002

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1015190932351

zbMATH Keywords

Jacobson radicalmatrix ringscategory equivalencesfunctorsendomorphism rings of Abelian groupstorsion-free groups of finite rankE-ringsrealization theoremsE-modulesquasi-endomorphisms

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30)

Related Items (27)

Finite automata and numbers ⋮ On Abelian groups with commuting monomorphisms. ⋮ On projectively soluble Abelian groups. ⋮ Abelian groups with nilpotent commutators of endomorphisms. ⋮ Abelian groups with normal endomorphism rings. ⋮ Abelian groups as UA-modules over their endomorphism ring. ⋮ On the Jacobson radical of the endomorphism ring of a homogeneous separable group. ⋮ Homogeneous maps of Abelian groups. ⋮ Hopficity of Modules and Rings (Survey) ⋮ Modules over discrete valuation domains. III ⋮ On L. Fuchs' problems 17 and 43. ⋮ Modules over discrete valuation domains. I ⋮ Abelian groups as endomorphic modules over their endomorphism ring. ⋮ Abelian groups with sufficiently \(\pi\)-regular endomorphism ring ⋮ The Jacobson radical of the endomorphism ring of a torsion-free Abelian group. ⋮ On the projective commutant of Abelian groups. ⋮ On the determinability of mixed abelian groups by their endomorphism semigroups ⋮ Fully invariant subgroups, full transitivity, and homomorphism groups of Abelian groups. ⋮ Isomorphisms of endomorphism semigroups of mixed abelian groups ⋮ Modules over discrete valuation domains. II ⋮ On definability of a periodic \(\text{EndE}^+\)-group by its endomorphism group. ⋮ Some classes of Hopfian Abelian groups. ⋮ Determination of the direct sums of rational groups by \(H\)-representations of the endomorphism rings up to equality ⋮ Local Abelian torsion-free groups. ⋮ On a direct sum of irreducible groups. ⋮ Hopfian algebraically compact Abelian groups. ⋮ Mixed abelian groups with isomorphic endomorphism semigroups.

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