• 제목/요약/키워드: (m, n)-quasi-ideal element

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ON ALMOST QUASI-COHERENT RINGS AND ALMOST VON NEUMANN RINGS

  • El Alaoui, Haitham;El Maalmi, Mourad;Mouanis, Hakima
    • 대한수학회보
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    • 제59권5호
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    • pp.1177-1190
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    • 2022
  • Let R be a commutative ring with identity. We call the ring R to be an almost quasi-coherent ring if for any finite set of elements α1, …, αp and a of R, there exists a positive integer m such that the ideals $\bigcap{_{i=1}^{p}}\;R{\alpha}^m_i$ and AnnRm) are finitely generated, and to be almost von Neumann regular rings if for any two elements a and b in R, there exists a positive integer n such that the ideal (αn, bn) is generated by an idempotent element. This paper establishes necessary and sufficient conditions for the Nagata's idealization and the amalgamated algebra to inherit these notions. Our results allow us to construct original examples of rings satisfying the above-mentioned properties.