대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제39권1호
  • /
  • Pages.93-104
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  • 2024
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ON STRONGLY QUASI J-IDEALS OF COMMUTATIVE RINGS

  • El Mehdi Bouba (Mathematics Department Faculty Multidisciplinary of Nador Mohammed First University) ;
  • Yassine EL-Khabchi (Department of Mathematics Faculty of Science University Moulay Ismail Meknes ) ;
  • Mohammed Tamekkante (Department of Mathematics Faculty of Science University Moulay Ismail Meknes )
  • 투고 : 2023.06.05
  • 심사 : 2023.08.08
  • 발행 : 2024.01.31
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초록

Let R be a commutative ring with identity. In this paper, we introduce a new class of ideals called the class of strongly quasi J-ideals lying properly between the class of J-ideals and the class of quasi J-ideals. A proper ideal I of R is called a strongly quasi J-ideal if, whenever a, b ∈ R and ab ∈ I, then a2 ∈ I or b ∈ Jac(R). Firstly, we investigate some basic properties of strongly quasi J-ideals. Hence, we give the necessary and sufficient conditions for a ring R to contain a strongly quasi J-ideals. Many other results are given to disclose the relations between this new concept and others that already exist. Namely, the primary ideals, the prime ideals and the maximal ideals. Finally, we give an idea about some strongly quasi J-ideals of the quotient rings, the localization of rings, the polynomial rings and the trivial rings extensions.

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참고문헌

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