Uniformly-S-pseudo-projective modules

2025/10/11 by adarbeh, Mohammad, Saleh, Mohammad
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.10170

Abstract

In this paper, we introduce the notion of uniformly-S-pseudo-projective (u-S-pseudo-projective) modules as a generalization of u-S-projective modules. Let R be a ring and S a multiplicative subset of R. An R-module P is said to be u-S-pseudo-projective if for any submodule K of P, there is s∈ S such that for any u-S-epimorphism f:P→ (P)/(K), sf can be lifted to an endomorphism g:P→ P. Some properties of this notion are obtained. For example, we prove that an R-module M is u-S-quasi-projective if and only if M⊕ M is u-S-pseudo-projective. A new characterization of u-S-semisimple rings is given in terms of this notion.

Citations

• Uniformly S-pseudo-injective modules
• Uniformly S-projective relative to a module and its dual
• Uniformly S-Noetherian rings
• Characterizing S-projective modules and S-semisimple rings by uniformity
• Characterizing S-flat modules and S-von Neumann regular rings by uniformity
• Dual automorphism-invariant modules

Cited by

• Uniformly S-projective relative to a module and its dual

Related

• Uniformly S-pseudo-injective modules
• Uniformly S-projective relative to a module and its dual
• Characterizing S-projective modules and S-semisimple rings by uniformity
• Pushouts and e-Projective Semimodules
• Uniformly S-essential submodules and uniformly S-injective uniformly S-envelopes