Abstract
A ring K is said to be a unique addition ring (UA-ring) if on its multiplicative semigroup (K, ·) it is possible to set only one binary operation of + turning (K, ·, +) into a ring. We call an Abelian group an End-UA-group if its endomorphism ring is a UA-ring. In this paper, End-UA-groups are found in a class of algebraically compact Abelian groups.
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