• 제목/요약/키워드: graded Jacobson radical

검색결과 2건 처리시간 0.014초

DECOMPOSITIONS OF GRADED MAXIMAL SUBMODULES

  • Moh'd, Fida
    • 대한수학회논문집
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    • 제37권1호
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    • pp.1-15
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    • 2022
  • In this paper, we present different decompositions of graded maximal submodules of a graded module. From these decompositions, we derive decompositions of the graded Jacobson radical of a graded module. Using these decompositions, we prove new theorems about graded maximal submodules, improve old theorems, and give other proofs for old theorems.

ON GRADED J-IDEALS OVER GRADED RINGS

  • Tamem Al-Shorman;Malik Bataineh;Ece Yetkin Celikel
    • 대한수학회논문집
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    • 제38권2호
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    • pp.365-376
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    • 2023
  • The goal of this article is to present the graded J-ideals of G-graded rings which are extensions of J-ideals of commutative rings. A graded ideal P of a G-graded ring R is a graded J-ideal if whenever x, y ∈ h(R), if xy ∈ P and x ∉ J(R), then y ∈ P, where h(R) and J(R) denote the set of all homogeneous elements and the Jacobson radical of R, respectively. Several characterizations and properties with supporting examples of the concept of graded J-ideals of graded rings are investigated.