The Research On S0-poset

Abstract In this thesis, we study fundamental theory of S-poset by order theory and S-act theory. In section 1,order congruence in S-poset is mfroduced, then three homomophisms fundamental theorem of S-poset is given by order congruence. In section 2,. The decomposition theorem of S-poset is given by strongly convex S-poset and the structure of projedive S-poset is given by the theorem .This structure theorem is generalization of projective S-act structure theorem[2],it is also better than theorem which was given in [6];Meanwhile, I- regular S-poset is investigated in this section. In section 3, The tenor product of S-poset is first introduced by a difference method of paper [5], we study order congruence class and order relationships over the tenor product Then we give out one necessary and sufficient condition is determined for a S-poset to be flat and prove that projeclive is flatness and pogroup is absolutely by condition called (1? which we introduce in this section; Finally when semigroup ~ is order regular, we prove all cyclic S-poset are flat and illuminate converse is fail by constructing a semigroup.