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Graded ϕ-2-Absorbing and Graded ϕ-2-Absorbing Primary Submodules
Mathematics ( IF 2.3 ) Pub Date : 2021-05-11 , DOI: 10.3390/math9101083 Azzh Saad Alshehry , Malik Bataineh , Rashid Abu-Dawwas
Mathematics ( IF 2.3 ) Pub Date : 2021-05-11 , DOI: 10.3390/math9101083 Azzh Saad Alshehry , Malik Bataineh , Rashid Abu-Dawwas
The main goal of this article is to explore the concepts of graded -2-absorbing and graded -2-absorbing primary submodules as a new generalization of the concepts of graded 2-absorbing and graded 2-absorbing primary submodules. Let be a function, where denotes the collection of graded R-submodules of M. A proper is said to be a graded -2-absorbing R-submodule of M if whenever are homogeneous elements of R and s is a homogeneous element of M with , then or or , and we call K a graded -2-absorbing primary R-submodule of M if whenever are homogeneous elements of R and s is a homogeneous element of M with , then or is in the graded radical of K or . Several properties of these new forms of graded submodules are investigated.
中文翻译:
分级吸收ϕ-2-和分级吸收-2-初级子模块
本文的主要目标是探索分级的概念 -2-吸收和分级 -2-吸收主子模块是对分2吸收和分2吸收主子模块概念的新概括。让 成为一个函数 表示M的渐变R-子模块的集合。正确的 据说是分级的 -2-吸收ř的-submodule中号如果每当 是均匀的元素- [R和小号是均匀的元件中号与 , 然后 或者 或者 ,我们称K为等级 -2-吸收初级ř的-submodule中号如果每当 是均匀的元素- [R和小号是均匀的元件中号与 , 然后 或者 在K的渐变根中或 。研究了这些新形式的渐变子模块的几个属性。
更新日期:2021-05-11
中文翻译:
分级吸收ϕ-2-和分级吸收-2-初级子模块
本文的主要目标是探索分级的概念