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<p>Let <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10587_2025_506_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\({\cal H}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mi mathvariant="script">H</mi> </mrow> </math></EquationSource> </InlineEquation> be the set of all commutative rings with unity whose nilradical is a divided prime ideal. The concept of maximal non-<i>ϕ</i>-Mori subrings of a ring is introduced to generalize the concept of maximal non-Mori subrings of domain. A proper subring <i>R</i> of a ring <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10587_2025_506_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\(T \in {\cal H}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mi>T</mi> <mo>∈</mo> <mrow> <mi mathvariant="script">H</mi> </mrow> </math></EquationSource> </InlineEquation> is called a maximal non-<i>ϕ</i>-Mori subring if <i>R</i> is not a <i>ϕ</i>-Mori ring but each subring of <i>T</i> properly containing <i>R</i> is a <i>ϕ</i>-Mori ring.</p>

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Maximal non-ϕ-Mori subrings of a ring

  • 期刊论文

  • 发表日期：

    2025年8月5日

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  • Rahul Kumar,
  • Anant Singh,
  • Atul Gaur

摘要

Let \({\cal H}\) H be the set of all commutative rings with unity whose nilradical is a divided prime ideal. The concept of maximal non-ϕ-Mori subrings of a ring is introduced to generalize the concept of maximal non-Mori subrings of domain. A proper subring R of a ring \(T \in {\cal H}\) T ∈ H is called a maximal non-ϕ-Mori subring if R is not a ϕ-Mori ring but each subring of T properly containing R is a ϕ-Mori ring.