Study On Abundant Semigroups And Fuzzy Regular Semigroups

" Semigroup Algebra Theory " which is implelled by computer science and information science and researched systemically for more than sixty years, has been become a distinctive and special subject embranchment of " algebra ". As is showed in the relation of " Semigroup theory " and " Group theory ", it is genereral accepted that of " Ring theory " and " Field theory ". This status are established not only the appearance of a passel of system research production, but also the form of a suit of particular system research thoughtway.Semigroup theoretician said: semigroup congruence theory is the part of most profound and splendid in semigroup algebra theory. In particular,after Zadeh introduced the concept of fuzzy set, fuzzy relations are appeared. Such as studying the structure theory of general semigroup, we can research the semigroup fuzzy properties by setting up semigroup fuzzy theory, including the theory of fuzzy congruence on semigroup and quotient semigroup theory which confirmed by fuzzy congruence relation. Kuroki generalized the semigroup homomorphism theory that is more ecumenical and content ample based this ideas. The gerenal semigroup congruence theory can not be researched easily. Recently, the researcher study the fuzzy congruence on inverse semogroup and some fuzzy properties on regular semigroup.This thesis is devoted to study the structure theory of abundant semigroup and fuzzy structure theory of regular semigroups by fuzzy congruence relation. Details are as follows:1. Because the Professor Xiaojiang Guo proved that any IC quasi-adequate semigroup is a type-W semigroup. Naturally, under the sense of the gerenlized regular semigroups, the structure of orthdox semigroup H(B, W_B/γ,Ψ) was established, depended heavily on the Hall's semigroup W_B with respect to a band B and the homomorphism γ between of inverse...