In this paper, we study the notions (strongly) soc-injective,(strongly) simple-injective and
(strongly) mininjective modules in σ [M]. For any module N in σ [M], N is strongly mininjective …

In this paper, we study the notions (strongly) soc-injective,(strongly) simple-injective and
(strongly) mininjective modules in σ [M]. For any module N in σ [M], N is strongly mininjective …

The purpose of this work is to investigate some more property of Q-finitely injective modules
and generalize this idea to Q-small finitely injective modules. A quasi-f-injective module Q is …

If M and N are right R-modules, M is called Socle-N-injective (Soc-N-injective) if every R-
homomorphism from the socle of N into M extends to N. Equivalently, for every semisimple …

We introduce and investigate ss-injectivity as a generalization of both soc-injectivity and
small injectivity. A module M is said to be ss-N-injective (where N is a module) if every R …

Let M and N be modules. Then N is said to be direct M-injective if every submodule of M that
is isomorphic to a direct summand of N is a direct summand of M. Also, we call N an M …

This paper introduce and investigate the notion of FI− M− principally injective and FI− semi-
injective (fully invariant-semi injective) modules. Clearly FI− semi-injective module does not …

In this note we show that a countable injective module is $\sum $-injective and consequently
a ring $ R $ is left noetherian if the category of left $ R $-modules has a countable injective …

In this paper we study MC-pseudo injective module which is the generalization of pseudo
injective module and we give an example of MC-pseudo injective module which is not M …

A module MR is called pseudo FQ-injective (or PFQ-injective for short) if every
monomorphism from a finitely generated submodule of M to M extends to an endomorphism …