arXiv subjects

Mohammad Adarbeh

Publications and source records attributed to Mohammad Adarbeh.

3 recordsLinked to original sources

arXiv2025

Uniformly S-pseudo-injective modules

This paper introduces the notion of uniformly-S-pseudo-injective (u-S-pseudo-injective) modules as a generalization of u-S-injective modules. Let R be a ring and S a multiplicative subset of R. An R-module E is said to be u-S-pseudo-injective if for any submodule K of E, there is s in S such that for any u-S-monomorphism f : K \to E, sf can be extended to an endomorphism g : E \to E. Several properties of this notion are studied. For example, we show that an R-module M is u-S-quasi-injective if and only if M \oplus M is u-S-pseudo-injective. Two classes of rings related to the class of QI-rings are introduced and characterized.

math.AC↗

arXiv2025

Uniformly S-essential submodules and uniformly S-injective uniformly S-envelopes

In this paper, we introduce the notion of uniformly S-essential (u-S-essential) submodules. Let R be a commutative ring, S a multiplicative subset of R, and M an R-module. A submodule N of M is said to be u-S-essential in M if for any submodule L of M, N \cap L is u-S-torsion implies L is u-S-torsion. Several properties of this notion are studied. We also introduce the notions of u-S-uniform modules and u-S-injective u-S-envelopes and characterize them in terms of u-S-essential submodules.

math.AC↗

arXiv2025

Uniformly S-projective relative to a module and its dual

In this article, we introduce the notion of uniformly S-projective (u-S-projective) relative to a module. Let S be a multiplicative subset of a ring R and M an R-module. An R-module P is said to be u-S-projective relative to M if for any u-S-epimorphism f : M \to N, the induced map HomR(P, f ): HomR(P, M ) \to HomR(P, N ) is a u-S-epimorphism. Dually, we also introduce u-S-injective relative to a module. Some properties of these notions are discussed. Several characterizations of u-S-semisimple modules are given in terms of these notions. The notions of u-S-quasi-projective and u-S-quasi-injective modules are also introduced, and some of their properties are discussed.

math.AC↗