E-Groups and E-Rings

• Published in: Journal 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
• Language: English
• 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

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...