Geodesic
A~note on pseudocongruences in semigroups
Lobachevskii journal of mathematics, Tome 11 (2002), pp. 19-21.

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In [1] we introduced the concept of pseudoorder in ordered semigroups and we proved that each pseudoorder on an ordered semigroup $S$ induces a congruence $\sigma$ on $S$ such that $S/\sigma$ is an ordered semigroup. In this short note we introduce the concept of pseudocongruence in semigroups and we prove that each pseudocongruence on a semigroup $S$ induces a congruence $\sigma$ on $S$ such that $S/\sigma$ is an ordered semigroup.
Keywords: ordered semigroup, pseudocongruence in semigroup. 
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N. Kehayopulu; M. Tsingelis. A~note on pseudocongruences in semigroups. Lobachevskii journal of mathematics, Tome 11 (2002), pp. 19-21. http://geodesic.mathdoc.fr/item/LJM_2002_11_a3/

[1] N. Kehayopulu and M. Tsingelis, “On subdirectly irreducible ordered semigroups”, Semigroup Forum, 50 (1995), 161–177 | DOI | MR | Zbl

[2] Xie Xiang-Yun, “Fuzzy ideal extensions of semigroups”, Soochow J. Math., 27:2 (2001), 125–138 | MR | Zbl