E-inversive semigroups with a completely simple kernel |
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Authors: | Roman S. Gigoń |
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Affiliation: | 1. Department of Mathematics, University of Bielsko-Biala, Bielsko-Bia?a, Polandrgigon@ath.bielsko.pl |
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Abstract: | We show that an E-inversive semigroup S has a completely simple kernel KS if and only if it contains a primitive idempotent (in that case, KS is the set-theoretic union of the groups eSe, where e is a primitive idempotent of S). Along the way, some equivalent conditions for a semigroup to be E-inversive are given. Moreover, some applications of the above theorem will be pointed out. |
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Keywords: | Completely simple kernel E-inversive semigroup kernel least idempotent local subsemigroup (m,n)-ideal primitive idempotent |
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