2021/02/20 by Ece Yetki̇n Çeli̇kel, Celikel, Ece Yetkin, Hani A. Khashan +1
Decision Sciences · Mathematics · #13A15 #13A18 #13A99 #Advanced Topics in Algebra #Commutative Algebra (math.AC) #FOS: Mathematics #Fuzzy and Soft Set Theory #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2102.10300
openalex publication_date 2021/02/20 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
Let R be a commutative ring with identity and M be a unitary R-module. The aim of this paper is to extend the notion of quasi J-ideals of commutative rings to quasi J-submodules of modules. We call a proper submodule N of M a quasi J-submodule if whenever r∈ R and m∈ M such that rm∈ N and r∉(J(R)M:M), then m∈ M-rad(N). We present various properties and characterizations of this concept (especially in finitely generated faithful multiplication modules). Furthermore, we provide new classes of modules generalizing presimplifiable modules and justify their relation with (quasi) J-submodules. Finally, for a submodule N of M and an ideal I of R, we characterize the quasi J-ideals of the idealization ring R(+)M.