Geodesic
Some characterizations of regularity and intra-regularity of $\Gamma$-semigroups by means of quasi-ideals
Novi Sad Journal of Mathematics, Tome 51 (2021) no. 2.

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The concept of regularity in $\Gamma$-semigroups is not very easy to deal with even though it shares some analogy with its analogue in semigroup theory. In this paper we establish a mechanism which translates the regularity in a $\Gamma$-semigroup $(S,\Gamma)$ as the usual von Neumann regularity in an ordinary semigroup $\Omega_{\gamma_{0}}$ that we construct in terms of $(S,\Gamma)$. This enables us to characterize the regularity in $\Gamma$-semigroups by means of quasi-ideals. A similar characterization is proved for those $\Gamma$-semigroups which are regular and intra-regular.
Publié le :
DOI : 10.30755/NSJOM.10795
Classification : 20M05, 20M10, 20M12, 20M17
Keywords: intra-regular $\Gamma$-semigroups, quasi-ideals, bi-ideals 
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     title = {Some characterizations of regularity and intra-regularity of $\Gamma$-semigroups by means of quasi-ideals},
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Fabiana Çullhaj; Anjeza Krakulli. Some characterizations of regularity and intra-regularity of $\Gamma$-semigroups by means of quasi-ideals. Novi Sad Journal of Mathematics, Tome 51 (2021) no. 2. doi : 10.30755/NSJOM.10795. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.10795/

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