FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1998, VOLUME 4, NUMBER 2, PAGES 763-767

Finiteness conditions for subdirectly irreducible $S$-acts and modules

I. B. Kozhukhov

Abstract

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It is proved that, for every semigroup $S$ of $n$ elements, the cardinalities of the subdirectly irreducible $S$-acts are less or equal to $2n+1$. If the cardinalities of the subdirectly irreducible $S$-acts are bounded by a natural number then $S$ is a periodic semigroup. It is obtained a combinatorial proof of the fact that there exist only finitely many of unitary subdirect irreducible modules over a finite ring.

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Last modified: June 17, 1998