Periodic Abelian Groups with $$UA$$ -Rings of Endomorphisms

Abstract

A ring \(R\) is said to be a unique addition ring (a \(UA\)-ring) if its multiplicative semigroup \((R,{\text{ }} \cdot )\) can uniquely be endowed with a binary operation \( +\) in such a way that \((R,{\text{ }} \cdot ,{\text{ }} + )\) becomes a ring. An Abelian group is said to be an \({\text{End - }}UA\)-group if the endomorphism ring of the group is a \(UA\)-ring. In the paper we study conditions under which an Abelian group is an \({\text{End - }}UA\)-group.