2022/03/09 by Mohammed Issoual, Najib Mahdou, Issoual, Mohammed +5
Mathematics · #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2203.04690
openalex publication_date 2022/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we introduce the notion of S-1-absorbing primary submodule as an extension of 1-absorbing primary submodule. Let S be a multiplicatively closed subset of a ring R and M be an R-module. A submodule N of M with (N:RM)∩ S=∅ is said to be S-1-absorbing primary if whenever abm∈ N for some non-unit a,b∈ R and m∈ M, then either sab∈(N:RM) or sm∈ M-rad(N). We examine several properties of this concept and provide some characterizations. In addition, S-1-absorbing primary avoidance theorem and S -1-absorbing primary property for idealization and amalgamation are presented.