Abstract
A ring K is called a unique addition ring (a UA-ring) if there exists a unique binary operation + on the multiplicative semigroup (K, · ) of K such that (K, ·, +) is a ring. We say that an abelian group is an End-UA-group if its endomorphism ring is a UA-ring. We find End-UA-groups in the class of completely decomposable quotient divisible abelian groups.
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