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 SM ISO690:2012DUDEK, Wieslaw, GIGON, Roman. Congruences on completely inverse AG-groupoids. In: Quasigroups and Related Systems, 2012, vol. 20, nr. 2(28), pp. 203-209. ISSN 1561-2848. |
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 Quasigroups and Related Systems |
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| Volumul 20, Numărul 2(28) / 2012 / ISSN 1561-2848 | ||||||
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By a completely inverse AG-groupoid we mean an inverse AG-groupoid A satisfying the identity xx−1 = x−1x, where x−1 denotes a unique element of A such that x = (xx−1)x and x−1 = (x−1x)x−1. We show that the set of all idempotents of such groupoid forms a semilattice and the Green's relations H,L,R,D and J coincide on A. The main result of this note says that any completely inverse AG-groupoid meets the famous Lallement's Lemma for regular semigroups. Finally, we show that the Green's relationH is both the least semilattice congruence
and the maximum idempotent-separating congruence on any completely inverse AG-groupoid. |
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<meta name="citation_title" content="Congruences on completely inverse AG-groupoids"> <meta name="citation_author" content="Dudek Wieslaw"> <meta name="citation_author" content="Gigon Roman"> <meta name="citation_publication_date" content="2012/07/02"> <meta name="citation_journal_title" content="Quasigroups and Related Systems"> <meta name="citation_volume" content="28"> <meta name="citation_issue" content="2"> <meta name="citation_firstpage" content="203"> <meta name="citation_lastpage" content="209"> <meta name="citation_pdf_url" content="https://ibn.idsi.md/sites/default/files/imag_file/Congruences%20on%20completely%20inverse%20AG%20groupoids.pdf">
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