FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1997, VOLUME 3, NUMBER 3, PAGES 869-878

Semigroups with right congruences of finite index

I. B. Kozhukhov

Abstract

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It is proved that all non-trivial right congruences of a semigroup $S$ have finite indices if and only if either $S$ is finite or $S$ is isomorphic to a subsemigroup of the additive group of integers with the adjoint zero. This result allows to describe the semigroup algebras whose non-trivial right ideals have the finite codimensions.

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