Let R be a ring with identity. Given a positive integer n, a unitary right R-module X is called n–
injective provided, for every n-generated right ideal A of R, every R-homomorphism φ: A→ X …

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 …

If M and N are right R-modules, M is called simple-N-injective if every R-homomorphism γ
from a submodule K of N into M with γ (K) simple extends to N. In this paper, a right R …

Abstract A right R–module E over a ring R is said to be maximally injective in case for any
maximal right ideal m of R, every R–homomorphism f: m→ E can be extended to an R …

Throughout this paper R will denote a ring with idenity element and M a unitary right module
over R. An R-module M is said to be direct injective if and only if given direct summand N of …

Let be a non-empty collection of right ideals of a ring R. A right R-module X is called-
injective provided each R-homomorphism ϕ: A→ X with A in can be lifted to an R …

ABSTRACT A principal right ideal of a ring is called uniquely generated if any two elements
of the ring that generate the same principal right ideal must be right associated (ie, if for all a …

A ring R is a right SI-ring if every singular right R-module is injective, while R is a right S3I-
ring if every singular semisimple right R-module is injective. In this paper, we investigate and …

In this article, 𝑅 is an associative ring with identity, and All R-modules are unital. We denote
𝑟𝑅 (𝜔) and 𝑙𝑅 (𝜔) to the right annihilator and the left annihilator of 𝜔, respectively. The set …

A ring R is called left IP-injective if every homomorphism from a left ideal of R into R with
principal image is given by right multiplication by an element of R. It is shown that R is left IP …