Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 3, pp. 869-878
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I. B. Kozhukhov. Semigroups with right congruences of finite index. Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 3, pp. 869-878. http://geodesic.mathdoc.fr/item/FPM_1997_3_3_a14/
@article{FPM_1997_3_3_a14,
author = {I. B. Kozhukhov},
title = {Semigroups with right congruences of finite index},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {869--878},
year = {1997},
volume = {3},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_1997_3_3_a14/}
}
TY - JOUR
AU - I. B. Kozhukhov
TI - Semigroups with right congruences of finite index
JO - Fundamentalʹnaâ i prikladnaâ matematika
PY - 1997
SP - 869
EP - 878
VL - 3
IS - 3
UR - http://geodesic.mathdoc.fr/item/FPM_1997_3_3_a14/
LA - ru
ID - FPM_1997_3_3_a14
ER -
%0 Journal Article
%A I. B. Kozhukhov
%T Semigroups with right congruences of finite index
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 1997
%P 869-878
%V 3
%N 3
%U http://geodesic.mathdoc.fr/item/FPM_1997_3_3_a14/
%G ru
%F FPM_1997_3_3_a14
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.
