On graded Jgr -classical 2-absorbing submodules of graded modules over graded commutative rings
نویسندگان
چکیده
منابع مشابه
On 2-absorbing Primary Submodules of Modules over Commutative Rings
All rings are commutative with 1 6= 0, and all modules are unital. The purpose of this paper is to investigate the concept of 2-absorbing primary submodules generalizing 2-absorbing primary ideals of rings. Let M be an R-module. A proper submodule N of an R-module M is called a 2-absorbing primary submodule of M if whenever a, b ∈ R and m ∈M and abm ∈ N , then am ∈M -rad(N) or bm ∈M -rad(N) or ...
متن کاملOn graded classical prime and graded prime submodules
Let $G$ be a group with identity $e.$ Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we introduce several results concerning graded classical prime submodules. For example, we give a characterization of graded classical prime submodules. Also, the relations between graded classical prime and graded prime submodules of $M$ are studied.
متن کاملon graded classical prime and graded prime submodules
let $g$ be a group with identity $e.$ let $r$ be a $g$-graded commutative ring and $m$ a graded $r$-module. in this paper, we introduce several results concerning graded classical prime submodules. for example, we give a characterization of graded classical prime submodules. also, the relations between graded classical prime and graded prime submodules of $m$ are studied.
متن کاملGraded Rings and Modules
1 Definitions Definition 1. A graded ring is a ring S together with a set of subgroups Sd, d ≥ 0 such that S = ⊕ d≥0 Sd as an abelian group, and st ∈ Sd+e for all s ∈ Sd, t ∈ Se. One can prove that 1 ∈ S0 and if S is a domain then any unit of S also belongs to S0. A homogenous ideal of S is an ideal a with the property that for any f ∈ a we also have fd ∈ a for all d ≥ 0. A morphism of graded r...
متن کاملOn Graded Weakly Classical Prime Submodules
Let R be a G-graded ring and M be a G-graded R-module. In this article, we introduce the concept of graded weakly classical prime submodules and give some properties of such submodules.
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ژورنال
عنوان ژورنال: Demonstratio Mathematica
سال: 2021
ISSN: 2391-4661
DOI: 10.1515/dema-2021-0015