Let R be a J-regular ring, ie, R/J (R) is a von Neumann regular ring, where J (R) is the
Jacobson radical of R. It is proved:(i) For every n≥ 1, R is right n-injective if and only if every …

We introduce the notion of semi-poor modules and consider the possibility that all modules
are either injective or semi-poor. This notion gives a generalization of poor modules that …

Let R be a ring. For two fixed positive integers m and n, a right R-module M is called (m, n)-
injective if every right R-homomorphism from an n-generated submodule of Rm to M extends …

Let be a finitely accessible category with products, and assume that its symmetric category is
also finitely accessible and pure semisimple. We study necessary and sufficient conditions …

An R-module F is called closed (neat) projective if, for every closed (neat) submodule L of
every R-module M, every homomorphism from F to M/L lifts to M. In this paper, we study …

Throughout this paper, R denotes an associative ring with identity and all modules are
unitary. A right R-module M is called principally injective briefly, p-injective) if for any …

In this note, we consider certain generalizations of injectivity and p-injectivity in connection
with von Neumann regular rings, self-injective regular rings, II-regular rings, semi-simple …

Introduction. Recently the concept of weakly injective modules due to [ll] has extensively
been studied and used to characterize various rings and modules; see [I-3, 5, 10-14, 16-18 …

Let $ R $ be a commutative ring and let $ S $ be an $ R $-algebra. It is well-known that if $ N
$ is an injective $ R $-module, then $\operatorname {Hom} _R (S, N) $ is an injective $ S …

Given modules M and N, M is said to be N-subinjective if for every extension K of N and
every homomorphism φ: N→ M there exists a homomorphism ϕ: K→ M such that ϕ| N= φ …