Uniformly S-pseudo-injective modules
Commutative Algebra
2026-02-04 v3
Abstract
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.
Keywords
Cite
@article{arxiv.2509.05843,
title = {Uniformly S-pseudo-injective modules},
author = {Mohammad Adarbeh and Mohammad Saleh},
journal= {arXiv preprint arXiv:2509.05843},
year = {2026}
}