W-P-flat Modules And W-P-injective Modules Over Commutative Rings And Their Applications

In this thesis,we study the w-module theoretic analogue of P-flat modules and P-injective modules in terms of w-module theory over commutative rings.In Chapter3,we introduce the concept of w-P-flat modules over commutative rings and discuss several characterizations and properties of this class of modules.As applications of w-P-flat modules,some new characterizations of von Neumann regular rings,PvMDs(Pr(?)fer v-multiplication domains)and DW domains are given.In this chapter,we also discuss two special classes of commutative rings,those are w-P.f rings(i.e.,commutative rings in which every principal ideal is w-P-flat)and p.p rings(i.e.,commutative rings in which every principal ideal is projective).In Chapter 4,we introduce the concept of w-P-injective modules over commutative rings and discuss several characterizations and properties of this class of modules.As applications of w-P-injective modules,some new characterizations of von Neumann regular rings,PvMDs,Krull domains and DW domains are given.In Chapter 5,we introduce the concept of w-P-coherent rings in terms of modules of finitely presented type and give several characterizations of these rings by using w-P-flat modules and w-P-injective modules.