Let n≥ 1 be an integer. A functor F∈(mod-R, Ab) is called n-strongly FP-injective if F is
isomorphic to some functor-⊗ M in (mod-R, Ab) with M an FP n-injective left R-module. A …

We study the existence of covers and envelopes by some special functors on the category of
finitely presented modules. As an application, we characterize some important rings using …

We introduce weakly FP-injective and weakly flat functors, and we show that a right R-
module K is FP-injective if and only if (−, K) is a flat weakly FP-injective functor in ((\rm mod …

In this paper, we develop relative homological algebra in the category of functors from
finitely presented modules to Abelian groups. More specifically, we introduce the concepts of …

In this paper, first we give the definition of F-copartial morphisms with an additive exact
substructure F of an exact structure E in an additive category A. Then, we study many …

Let R be a ring with 1# 0. R-Mod (resp. Mod-R} denotes the category of left (resp. rrght) R-
modules. Throughout the entrre article full subcategories of R-Mod (resp. Mod-R) will be …

Let R be an associative ring with identity, m and n be fixed positive integers. The notions of
(m, n)-injective functors and (m, n)-flat functors are introduced. Some properties of these two …

We show that an N-complex of modules C is FP-injective if and only if C is N-exact and Z ni
(C) is an FP-injective module for each i= 1, 2,⋯, N and each n∈ Z by virtue of Gaussian …

Müller generalized in [12] the notion of a Frobenius extension to left (right) quasi-Frobenius
extension and proved the endomorphism ring theorem for these extensions. Recently, Guo …

Let $\Lambda $ and $\Gamma $ be Artin algebras, $ M $ a $\Gamma-\Lambda $-bimodule,
and $ R $ the triangular matrix ring of $\Lambda,\Gamma $, and $ M $; assume that $ R $ is …