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<p>It is shown that, for a strongly <i>ϕ</i>-pseudo-valuation ring, which is nonnil-coherent, the only possible values of the <i>ϕ</i>-weak global dimension are 0<i>,</i> 1<i>,</i> and ∞<i>.</i> We then provide necessary and sufficient conditions for a strongly <i>ϕ</i>-pseudo-valuation ring to be nonnil-coherent. As an application of these findings, we demonstrate that if <i>R</i> is a strongly nonnil-coherent <i>ϕ</i>-pseudo-valuation ring, then any overring <i>B</i> of <i>R</i> is also a nonnil-coherent <i>ϕ</i>-pseudo-valuation ring.</p>

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The ϕ-Weak Dimension of ϕ-Pseudo-Valuation Rings

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • Hwankoo Kim,
  • Najib Mahdou,
  • El Houssaine Oubouhou

摘要

It is shown that, for a strongly ϕ-pseudo-valuation ring, which is nonnil-coherent, the only possible values of the ϕ-weak global dimension are 0, 1, and ∞. We then provide necessary and sufficient conditions for a strongly ϕ-pseudo-valuation ring to be nonnil-coherent. As an application of these findings, we demonstrate that if R is a strongly nonnil-coherent ϕ-pseudo-valuation ring, then any overring B of R is also a nonnil-coherent ϕ-pseudo-valuation ring.