The Relative Research Of X-Ding Projective Modules And Y-Ding Injective Modules

Let R be an associative ring with identity and X is a class that contains all flat R-modules and Y is a class that contains all FP-injective modules.In chapter three,The definitions and the relative properties of X-Ding projective modules and Y-Ding injective modules are introduced and studied,and some properties of X-Ding projective modules(Y-Ding injective modules)over Frobenius extensions are studied.It is proven that(1)if GX-Dpd(R)<∞,then(X-DP(R),(X-DP(R))is a complete hereditary cotorsion pair;(2)if X is preenveloping and projectively resolving,then(X-DP(R),(X-DP(R))⊥)is a hereditary cotorsion pair for any injective module I,where X-pdR(I)<∞.In chapter four,the relative properties of definitions and dimensions of X-Ding projective complexes are introduced and studied.