대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제39권3호
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  • Pages.623-642
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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 ϕ-(n, d) RINGS AND ϕ-n-COHERENT RINGS

  • Younes El Haddaoui (Modelling and Mathematical Structures Laboratory Department of Mathematics Faculty of Science and Technology of Fez University) ;
  • Hwankoo Kim (Division of Computer Engineering Hoseo University) ;
  • Najib Mahdou (Modelling and Mathematical Structures Laboratory Department of Mathematics Faculty of Science and Technology of Fez University)
  • 투고 : 2023.11.16
  • 심사 : 2024.02.29
  • 발행 : 2024.07.31
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초록

This paper introduces and studies a generalization of (n, d)-rings introduced and studied by Costa in 1994 to rings with prime nilradical. Among other things, we establish that the ϕ-von Neumann regular rings are exactly either ϕ-(0, 0) or ϕ-(1, 0) rings and that the ϕ-Prüfer rings which are strongly ϕ-rings are the ϕ-(1, 1) rings. We then introduce a new class of rings generalizing the class of n-coherent rings to characterize the nonnil-coherent rings introduced and studied by Bacem and Benhissi.

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과제정보

The authors would like to thank the reviewer for his/her comments. H. Kim was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (2021R1I1A3047469).

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