Semigroup S-systems Theory And Fuzzy Algebraic Theory The Results

This thesis consists of two chapters.In chapter 1, we obtain some results about S—acts. Firstly, if sN is a subact of SM, then the lattice of the subacts of M containing N is lattice isomorphic to the lattice of the subacts of the factor act M/λ_N, where λ_N is the Rees congruence on M. Some isomorphism theorems of S—acts are also given. Secondly, we obtain two equivalent conditions for which a set M is biact SM_t. Finally, we obtain another characterization of coproduct of a family of S—acts and show that an S—act is projective if and only if it contains a dual basis.In chapter 2, we study some results about fuzzy algebra. If L is a complete ditributive lattice, the group G/A containing cosets of an L— fuzzy normal subgroup A of a group G is isomorphic to a factor group of G in a natural way; if f : Gâ†' G' is a group epimorphism, then there exists a one-to-one order-preserving correspondence between the L— fuzzy normal subgroups of G' and those of G which are constant on the kernel of f.