Applications Of Homomorphism On The Structure Of Semigroup

This paper describes the application of homomorphism on the structure of several types of semigroups, A semilattice decomposition is given for the structure of the regular group, the regular cipher and the abundant semigroup, and the regular cipher.The following are the main contents and conclusions:The definition and the related properties of the regular code group are given.Use of homomorphic mapping study its structure, and use of regular band and a right quasi-normal band with semi-rectangular grid study decomposition, with strong promotion of formal decomposition of semilattice grid decomposition.By utilizing homomorphisms and G-strong semilattice of semigroups, we show that the (*,～)Green-relation H*,～ is a regular band congruence on a r-ample semigroup if and only if it is a G- strong semilattice of completely J*,～- simple semigroups. The result generalizes Petrich’s result on completely regular semigroups with Green’s relation H a normal band congruence or a regular band congruence from the round of regular semigroups to the round of r-ample semigroups.The fifth chapter study *-weakly regular algebraic properties associated semigroup and the Regular *-Semigroup on some of the results which extended to also proved its class is D-square.Use (*,-)-Relationship regular password semigroup, homomorphic mapping θ,α,β θαβ and semilattice structure between the regular password-related algebraic properties of semigroups extended to *- regular semigroups super password.Discussion on a completely J*,～- simple semigroup condition, H* congruence in *- Password Super semigroups semilattice decomposition under strength, and its associated semilattice decomposition corresponding comparison.