STRONGLY ORTHODOX CONGRUENCES ON AN -INVERSIVE SEMIGROUP
Xingkui Fan, Qianhua Chen · Journal of the Australian Mathematical Society · 2013
Abstract In this paper we investigate some subclasses of strongly regular congruences on an $E$ -inversive semigroup $S$ . We describe the minimum and the maximum strongly orthodox congruences on $S$ whose characteristic trace coincides with the characteristic trace of given congruences and, in each case, we present an alternative characterization for them. A description of all strongly orthodox congruences on $S$ with characteristic trace $\tau $ is given. Further, we investigate the kernel relation of strongly orthodox congruences on an $E$ -inversive semigroup and give the least and the greatest element in the class of the same kernel with a given congruence.