2021/04/13 by Hani A. Khashan, Khashan, Hani A., Ece Yetki̇n Çeli̇kel +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2104.06134
openalex publication_date 2021/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a commutative ring with identity and M be a unitary R-module. By J(R), we denote the Jacobson radical of R. The purpose of this paper is to introduce the concept of weakly J-submodules generalizing J-submodules. We call a proper submodule N of M a weakly J-submodule if whenever 0≠ rm∈ N for r∈ R and m∈ M, then r∈(J(R)M:M) or m∈ N. Various properties and characterizations of weakly J-submodules are investigated especially in the case of multiplication modules.