FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1998, VOLUME 4, NUMBER 4, PAGES 1419-1422

Separable torsion free abelian groups with UA-rings of endomorphisms

O. V. Lyubimcev

Abstract

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A semigroup $(R,\; \cdot \; )$ is said to be a unique addition ring (UA-ring) if there exists a unique binary operation $+$, making $(R,\; \cdot \; ,+)$ into a ring. We call an abelian group $\$\backslash mathop\{End\}\$$-UA-group if its endomorphism ring is UA-ring. As a result we have obtained a characterization of separable tortion free $\$\backslash mathop\{End\}$-UA-groups.

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Last modified: January 25, 1999