Geodesic
Semigroups with right congruences of finite index
Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 3, pp. 869-878

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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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     author = {I. B. Kozhukhov},
     title = {Semigroups with right congruences of finite index},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1997_3_3_a14/}
}
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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/