E-groups and E-rings P. A. Krylov, A. A. Tuganbaev, A. V. Tsarev
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ArticleContent type: Текст Media type: электронный Subject(s): абелевы группы | кольца эндоморфизмов | E-замкнутые группы | E-группы | E-кольца | T-кольца | факторно делимые группыGenre/Form: статьи в журналах Online resources: Click here to access online
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Journal of mathematical sciences Vol. 256, № 3. P. 341-361Abstract: 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: E-closed groups, T -rings, A-rings, the groups admitting only commutative multiplications, etc.
Библиогр.: 36 назв.
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: E-closed groups, T -rings, A-rings, the groups admitting only commutative multiplications, etc.
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