SOME RESULTS ON THE LOCALLY EQUIVALENCE ON A NON-REGULAR SEMIGROUP Atlihan, Sevgi;
On any semigroup S, there is an equivalence relation , called the locally equivalence relation, given by a for all , . In Theorem 4 , Tiefenbach has shown that if is a band congruence, then := is a group. We show in this study that := is also a group whenever a is any idempotent element of S. Another main result of this study is to investigate the relationships between and in terms of semigroup theory, where may not be a band congruence.
J. M. Howie, Fundamentals of Semigroup Theory, Clarendon Press, 1995.
F. Pastijn, Regular locally testable semigroup as semigroups of quasi-ideals, Acta Math. Acad. Sci. Hungar. 36 (1980), no. 1-2, 161-166.
A. Tiefenbach, Locale Unterhalbgruppen, Ph. D. Thesis, University of Vienna, 1995.
A. Tiefenbach, On certain varieties of semigroups, Turkish J. Math. 22 (1998), no. 2, 145-152.