Some Studies On The Super-r-wide Semigroups

The semigroup theory is an important branch of algebra,which is widely used in the fields of formal language,graph theory,symbolic dynamics,heoretical computer science and information science.The semigroup congruence theory is important research direction of semigroup theory.On the one hand,the congruence of any semigroup gives us some imformation about the semigroup homorphism.On the other hand,almost all of the semigroup structure theorems depend on the important congruence of these semigroups.This paper mainly studies properties of super-r-wide semigroup and(*,?)?good congruence of some special super-r-wide semigroup.Firstly,we give some equivalent characterization of super-r-wide semigroup by using some axiomatic conditions and using the Malcev product.Secondly,based on the normal Rees matrix representation of the completely J*,?-simple semigroup by C.M.Gong etc.,we give a characterization of(*,?)-good congruence on completely J*,?-simple semigroup.Moreover,the intersection and union operation of(*,?)-good congruence are studied on completely J*,?-simple semigroup.Finally,we give a characterization of any(*,?)-g-ood congruence on normal crypto super-r-wide semigroup with the help of the strong semilattice decomposition theorem of the normal crypto super-r-wide semigroup.