2025/09/06 by Mohammad Adarbeh, Mohammad Saleh, Adarbeh, Mohammad +1 · 1 citation
Mathematics · Computer Science · #Rings, Modules, and Algebras #Advanced Algebra and Logic
paper · pdf · doi:10.48550/arxiv.2509.05843
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 → E, sf can be extended to an endomorphism g : E → 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 ⊕ M is u-S-pseudo-injective. Two classes of rings related to the class of QI-rings are introduced and characterized.