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<p>A commutative ring <i>R</i> with identity is called an <i>SV-ring</i> (respectively, <i>SPV-ring</i>) if the integral domain <i>R</i>/<i>P</i> is valuation (respectively, pseudo-valuation), for all prime ideals <i>P</i> of <i>R</i>. The main goal of this paper is to examine the behavior of the (locally) SV-ring and SPV-ring properties in various distinguished constructions.</p>

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On some valuation-like rings in certain ring extensions

  • 期刊论文

  • 发表日期：

    2025年9月5日

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  • Abdeslam Mimouni,
  • Omar Ouzzaouit,
  • Ali Tamoussit

摘要

A commutative ring R with identity is called an SV-ring (respectively, SPV-ring) if the integral domain R/P is valuation (respectively, pseudo-valuation), for all prime ideals P of R. The main goal of this paper is to examine the behavior of the (locally) SV-ring and SPV-ring properties in various distinguished constructions.