2024/06/04 by Driss Bennis, Bennis, Driss, Ayoub Bouziri +1
Computer Science · Mathematics · #13C11 #13C13 #13E99 #Advanced Algebra and Logic #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2406.02041
openalex publication_date 2024/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a commutative ring with identity, and let S be a multiplicative subset of R. In this paper, we introduce the notion of S-injective modules as a weak version of injective modules. Among other results, we provide an S-version of Baer's characterization of injective modules. We also present an S-version of Lambek's characterization of flat modules: an R-module M is S-flat if and only if its character, Homℤ(M, ℚ/ℤ), is an S-injective R-module. As applications, we establish, under certain conditions, S-counterparts of the Cartan--Eilenberg-Bass and Cheatham--Stone characterizations of Noetherian rings.