Weak injective covers and dimension of modules

Homological Properties of Modules with Finite Weak Injective and Weak Flat Dimensions

“…In Section 3, as some applications, we characterize the weak flat dimension of modules in terms of the relative derived functor Ext WF n (−, −) which completes the analogous results of Gao and Huang in [9].…”

“…By [9,Prop. 4.4], an R-module M is weak injective if and only if the map Ext WI 0 (M, N ) → Hom R (M, N ) is an epimorphism for every R-module N .…”

“…Since M ∈ WI ≤n , Ext n+1 R (F, M ) = 0. Moreover, wid R (L) ≤ n + 1 by (9) and [11,Thm. 3.8(2)], and hence Ext n+2 R (F, L) = 0.…”

“…Since every projective right R-module is weak flat, this complex is also exact. ) may be computed by using a right WF -resolution of M or a left WF -resolution of N .We also recall from[9, Sec. 5] that the functor − ⊗ R − is right balanced on M R × R M by WF × WI.…”

Weak Injective and Weak Flat Complexes

“…flat) as R-modules for any m ∈ Z; In [25,23], Liu et al introduced the notion of FP-injective complexes, they obtained many nice characterizations of them over coherent rings, and they showed that some properties of injective complexes have counterparts for FP-injective complexes. More recently, we introduced and investigated in [16,14] weak injective and weak flat modules, and generalized many results from coherent rings to arbitrary rings. In this process finitely presented modules were replaced by super finitely presented modules.…”