Uniformly S-essential submodules and uniformly S-injective uniformly S-envelopes
Commutative Algebra
2026-01-21 v2
Abstract
In this paper, we introduce the notion of uniformly S-essential (u-S-essential) submodules. Let R be a commutative ring and S a multiplicative subset of R. A submodule K of an R-module M is said to be u-S-essential in M if for any submodule L of M, s1(K \cap L) = 0 for some s1 \in S implies s2L = 0 for some s2 \in S. Several properties of this notion are studied. The notions of a u-S-uniform module and a u-S-injective u-S-envelope are also introduced, and we show that these notions are characterized by u-S-essential submodules.
Keywords
Cite
@article{arxiv.2509.01638,
title = {Uniformly S-essential submodules and uniformly S-injective uniformly S-envelopes},
author = {Mohammad Adarbeh and Mohammad Saleh},
journal= {arXiv preprint arXiv:2509.01638},
year = {2026}
}