FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

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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