FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1998, VOLUME 4, NUMBER 4, PAGES 1335-1344

Semigroups over which all acts are residually finite

I. B. Kozhukhov

Abstract

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The properties (*) and (**) of semigroup $S$ are investigated, namely: (*) every subdirectly irreducible right $S$-act is finite; (**) the cardinalities of subdirectly irreducible right $S$ acts are bounded by a natural number. We prove that if $S$ is a nilsemigroup then then these conditions are equivalent to each other and to finiteness of $S$. We characterize the commutative semigroups satisfying (**).

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