The Generalizations Of Strong Flatness S-Posets

Strong flatness S-posets is a class of important S-posets in S-posets category.In this thesis,we give the definition of condition(EP),condition(P'?)and condi-tion(P')in S-posets,and we use some counterexamples illustrate these conditions are the proper generalizations of strong flatness S-posets.Firstly we utilize these generalizations to study the properties of pomonoids,such as free,projective gener-ators,weak flatness and principal weak flatness,and give some characterization of pomonoids by these conditions.Then,the condition(EP)is characterized by in-troducing some pure homomorphisms,and we proved S-posets satisfying condition(EP)are closed under directed colimits.Also we prove S-posets A(J)satisfy the condition(EP)and give a sufficient and necessary condition of right S-posets A(J)satisfying condition(P'?),this provide theoretical basis for investigating some pomonoids.Finally,direct products of S-posets satisfying these conditions are considered...