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 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.