2024/01/16 by Zeynep Yılmaz Uçar, Bayram Alì Ersoy, Uçar, Zeynep Yılmaz +7
Mathematics · #13A15 #13C05 #13C13 #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2403.19659
openalex publication_date 2024/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study weakly classical 1-absorbing prime submodules of a nonzero unital module M over a commutative ring R having a nonzero identity. A proper submodule N of M is said to be a weakly classical 1-absorbing prime submodule, if for each m∈ M and nonunits a,b,c∈ R, 0≠ abcm∈ N implies that abm∈ N or cm∈ N. We give various examples and properties of weakly classical 1-absorbing prime submodules. Also, we investiage the weakly classical 1-absorbing prime submodules of tensor product F⊗ M of a (faithfully) flat R-module F and any R-module M. Also, we prove that if every proper submodule of an R-module M is weakly classical 1-absorbing prime, then Jac(R)3M=0. In terms of this result, we characterize modules over local rings in which every proper submodule is weakly classical 1-absorbing prime.