대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제39권3호
  • /
  • Pages.611-622
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  • 2024
  • /
  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ON NONNIL-m-FORMALLY NOETHERIAN RINGS

  • Abdelamir Dabbabi (Mathematics Department Faculty of Sciences of Monastir) ;
  • Ahmed Maatallah (Mathematics Department Faculty of Sciences of Monastir)
  • 투고 : 2023.11.06
  • 심사 : 2024.05.10
  • 발행 : 2024.07.31
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초록

The purpose of this paper is to introduce a new class of rings containing the class of m-formally Noetherian rings and contained in the class of nonnil-SFT rings introduced and investigated by Benhissi and Dabbabi in 2023 [4]. Let A be a commutative ring with a unit. The ring A is said to be nonnil-m-formally Noetherian, where m ≥ 1 is an integer, if for each increasing sequence of nonnil ideals (In)n≥0 of A the (increasing) sequence (∑i1+⋯+im=nIi1Ii2⋯Iim)n≥0 is stationnary. We investigate the nonnil-m-formally Noetherian variant of some well known theorems on Noetherian and m-formally Noetherian rings. Also we study the transfer of this property to the trivial extension and the amalgamation algebra along an ideal. Among other results, it is shown that A is a nonnil-m-formally Noetherian ring if and only if the m-power of each nonnil radical ideal is finitely generated. Also, we prove that a flat overring of a nonnil-m-formally Noetherian ring is a nonnil-m-formally Noetherian. In addition, several characterizations are given. We establish some other results concerning m-formally Noetherian rings.

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과제정보

The authors would like to thank the referee for his/her valuable comments which helped us improve the presentation of our paper.

참고문헌

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