Some Studies Of Good Congruences On Two Kinds Of Super R-wide Semigroups

The congruence theory of semigroups is an important research direction of semigroup algebra theory.About congruence theory of regular semigroups,a series of important results are obtained,forming the so-called kernel trace method.However,this method is not suitable for super-r-wide semigroups.Therefore,we need to explore new methods 0study congruence on super-r-wide semigroups.The main research of this paper are the good congruences on regular ortho-u-monoids and regular cryptic super r-wide semigroups,and study some properties on super r-wide semigroups.Firstly,based on the semi-spined product structure of regular ortho-u-monoids,the(~)-good congruences on u-Clifford semigroups are studied.Then by defining(~)-good congruence pairs,the(~)-good congruences on regular ortho-u-monoids are characterized.Secondly,by using the(*,~)-Green's relations,we investigated some properties on super r-wide semigroups.At last,by means of the quasi-strong semilattice decompsition theorem of regular cryptic super r-wide semigroups,the(*,~)-good comgruences on regular cryptic super r-wide semigroups are characterized.