In this paper, the notion of strongly G_C-projective and injective modules is introduced,
where C is a semidualizing module. Using these modules we can obtain a new …

A ring extension is a ring homomorphism preserving identities. In this paper, we give the
definition of relatively free modules on ring extensions and develop some basic properties of …

Given modules M and N, M is said to be N-subprojective if for every epimorphism g: B→ N
and homomorphism f: M→ N, there exists a homomorphism h: M→ B such that gh= f. For a …

In this paper, we introduce and study the concepts of weak n-injective and weak n-flat
modules in terms of super finitely presented modules whose projective dimension is at most …

We investigate the interplay between properties of Ext modules and the ascent of module
structures along local ring homomorphisms. Specifically, let $\varphi\colon (R,\mathfrak {m} …

We introduce the concepts of (n, d)-injective and (n, d)-flat as generalizations of injective, flat
modules and homological dimensions, and use them to characterize right n-coherent rings …

In this paper, we introduce the notion of Wn-modules and describe non-commutative
coherent rings with finite FP-selfinjective dimension. The obtained results generalize the …

Given modules RM and AR, RM is said to be absolutely AR-pure if A⊗ M→ A⊗ B is a
monomorphism for every extension RB of RM. For a module AR, the absolutely pure domain …

We show that, if T is a selfsmall and selforthogonal module over a noetherian ring R of finite
global dimension with the endomorphism ring A, then fdTA⩽ gdA⩽ idRT+ fdTA. Applying the …