On graded $ s $-prime submodules
Copyright policy )On graded $ s $-prime submodules
<abstract> <p>In this article, we introduce the concepts of graded $ s $-prime submodules which is a generalization of graded prime submodules. We study the behavior of this notion with respect to graded homomorphisms, localization of graded modules, direct product, and idealization. We succeeded to prove the existence of graded $ s $-prime submodules in the case of graded-Noetherian modules. Also, we provide some sufficient conditions for the existence of such objects in the general case, as well as, in the particular case of a grading by a finite group, polycyclic-by-finite group, or by $ \mathbb{Z} $, in addition to the interesting case of crossed product grading, which includes the class of group rings.</p> </abstract>
- Yarmouk University Jordan
Study of properties and structures of commutative rings, Deformations and Structures of Hom-Lie Algebras, Cluster Algebras and Triangulated Categories, Generalization, graded multiplication modules, 16W50, 13A02, graded prime submodule, Commutative Algebra (math.AC), graded s-prime submodules, Mathematical analysis, graded-noetherian modules, Noetherian, Graded ring, Prime (order theory), QA1-939, FOS: Mathematics, graded \(S\)-prime submodule, Algebra over a field, Algebra and Number Theory, Graded rings and modules (associative rings and algebras), Pure mathematics, crossed product grading, graded-Noetherian module, Mathematics - Rings and Algebras, graded prime submodules, Gradings, Mathematics - Commutative Algebra, Graded rings, Rings and Algebras (math.RA), Combinatorics, Physical Sciences, Homomorphism, Geometry and Topology, graded multiplication module, Mathematics
Study of properties and structures of commutative rings, Deformations and Structures of Hom-Lie Algebras, Cluster Algebras and Triangulated Categories, Generalization, graded multiplication modules, 16W50, 13A02, graded prime submodule, Commutative Algebra (math.AC), graded s-prime submodules, Mathematical analysis, graded-noetherian modules, Noetherian, Graded ring, Prime (order theory), QA1-939, FOS: Mathematics, graded \(S\)-prime submodule, Algebra over a field, Algebra and Number Theory, Graded rings and modules (associative rings and algebras), Pure mathematics, crossed product grading, graded-Noetherian module, Mathematics - Rings and Algebras, graded prime submodules, Gradings, Mathematics - Commutative Algebra, Graded rings, Rings and Algebras (math.RA), Combinatorics, Physical Sciences, Homomorphism, Geometry and Topology, graded multiplication module, Mathematics
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