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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.
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참고문헌 (4)
참고문헌 신청
A. Tiefenbach / 1995 / Locale Unterhalbgruppen / 박사 / University of Vienna
A. Tiefenbach / 1998 / On certain varieties of semigroups / Turkish J. Math 22 (2) : 145 ~ 152
F. Pastijn / 1980 / Regular locally testable semigroup as semigroups of quasi-ideals / Acta Math. Acad. Sci. Hungar 36 (1) : 161 ~ 166
J. M. Howie / 1995 / Fundamentals of Semigroup Theory / Clarendon Press
A. Tiefenbach / 1998 / On certain varieties of semigroups / Turkish J. Math 22 (2) : 145 ~ 152
F. Pastijn / 1980 / Regular locally testable semigroup as semigroups of quasi-ideals / Acta Math. Acad. Sci. Hungar 36 (1) : 161 ~ 166
J. M. Howie / 1995 / Fundamentals of Semigroup Theory / Clarendon Press
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