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Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Open Access Research Article

Graded Le-Jgr-prime submodules in commutative graded rings

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pp. 1297–1305Vol. 29Issue 3March 2026DOI: 10.47974/JDMSC-2458 Crossmark XML
Received:
04 Mar 2025
Published Online:
13 Feb 2026
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2458
Pages:
1297–1305

Abstract

In this paper, we introduce the concept of gr-Le-Jgr-PSub in the context of graded commutative rings and graded modules. These submodules extend and unify the properties of gr-Le-PSub and gr-J_gr-PSub through a fixed gr-Id L=⊕g∈Ω Lg. The research develops foundational definitions, proves equivalences, and examines the structural implications of these submodules under various module-theoretic operations, including localization, direct products, and quotient modules. Examples are provided to illustrate the distinct nature of graded Le-Jgr-prime submodules compared to other graded submodules. Furthermore, conditions under which these submodules exhibit maximal and semisimple properties are characterized, contributing new insights to the theory of graded modules. 

Keywords

Subject Classifications

13A0216W50

References

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