Some results on the locally equivalence on a non-regular semigroup
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On any semigroup S, there is an equivalence relation ΦS,called the locally equivalence relation, given by a ΦSb , aSa = bSb forall a, b 2 S. In Theorem 4 [4], Tiefenbach has shown that if ΦS is a bandcongruence, then Ga := [a]ΦS \ (aSa) is a group. We show in this studythat Ga := [a]ΦS \ (aSa) is also a group whenever a is any idempotentelement of S. Another main result of this study is to investigate therelationships between [a]ΦS and aSa in terms of semigroup theory, where ΦS may not be a band congruence.
Abstract
On any semigroup S, there is an equivalence relation ΦS,called the locally equivalence relation, given by a ΦSb , aSa = bSb forall a, b 2 S. In Theorem 4 [4], Tiefenbach has shown that if ΦS is a bandcongruence, then Ga := [a]ΦS \ (aSa) is a group. We show in this studythat Ga := [a]ΦS \ (aSa) is also a group whenever a is any idempotentelement of S. Another main result of this study is to investigate therelationships between [a]ΦS and aSa in terms of semigroup theory, where ΦS may not be a band congruence.
참고문헌 (4)
- J. M. Howie, "Fundamentals of Semigroup Theory" (1995), Clarendon Press
- F. Pastijn, "Regular locally testable semigroup as semigroups of quasi-ideals", Acta Math. Acad. Sci. Hungar, 36(1), pp.161~166 (1980)
- A. Tiefenbach, "Locale Unterhalbgruppen", 박사, pp.1995
- A. Tiefenbach, "On certain varieties of semigroups", Turkish J. Math, 22(2), pp.145~152 (1998)