E-Groups and E-Rings

An associative ring R is called an E-ring if the canonical homomorphism R ≅ E( R + ) is an isomorphism. Additive groups of E -rings are called E-groups . In other words, an Abelian group A is an E -group if and only if A ≅ End A and the endomorphism ring E( A ) is commutative. In this paper, we give...

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Published inJournal of mathematical sciences (New York, N.Y.) Vol. 256; no. 3; pp. 341 - 361
Main Authors Krylov, P. A., Tuganbaev, A. A., Tsarev, A. V.
Format Journal Article
LanguageEnglish
Published New York Springer US 04.07.2021
Springer
Springer Nature B.V
Subjects
Associativity
Electronic discussion groups
Group theory
Homomorphisms
Isomorphism
Mathematics
Mathematics and Statistics
Rings (mathematics)
Surveys
Abelian group
ring
quotient divisible group
endomorphism ring
20Kxx
closed group
group
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Summary:An associative ring R is called an E-ring if the canonical homomorphism R ≅ E( R + ) is an isomorphism. Additive groups of E -rings are called E-groups . In other words, an Abelian group A is an E -group if and only if A ≅ End A and the endomorphism ring E( A ) is commutative. In this paper, we give a survey of the main results on E -groups and E -rings and also consider some of their generalizations: ε -closed groups, T -rings, A -rings, the groups admitting only commutative multiplications, etc.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05430-2