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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published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/98/982/98222h.htm

Last modified: June 17, 1998