Scholarlink

<p>Let <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2917_Article_IEq1.gif" Format="GIF" Height="43" Rendition="HTML" Resolution="72" Type="Linedraw" Width="97" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Lambda =\begin{pmatrix} A &amp; 0\\ U &amp; B \end{pmatrix}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Λ</mi> <mo>=</mo> <mfenced close=")" open="("> <mrow> <mtable> <mtr> <mtd> <mi>A</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow /> <mi>U</mi> </mrow> </mtd> <mtd> <mi>B</mi> </mtd> </mtr> </mtable> </mrow> </mfenced> </mrow> </math></EquationSource> </InlineEquation> be a formal triangular matrix ring where <i>A</i>,&#xa0;<i>B</i> are rings and <i>U</i> is a (<i>B</i>,&#xa0;<i>A</i>)-bimodule. In this paper, we study some special classes over the formal triangular matrix ring <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2917_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Λ</mi> </math></EquationSource> </InlineEquation>. Further, using these special classes, we construct a left (resp. right) <i>n</i>-cotorsion pair over the formal triangular matrix ring <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2917_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Λ</mi> </math></EquationSource> </InlineEquation> from left (resp. right) <i>n</i>-cotorsion pairs over <i>A</i> and <i>B</i>. Finally, we give an example to illustrate our main results.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

n-Cotorsion Pairs Over Formal Triangular Matrix Rings

  • 期刊论文

  • 发表日期：

    2025年7月22日

查看全文
  • Taolue Long,
  • Xiaoxiang Zhang

摘要

Let \(\Lambda =\begin{pmatrix} A & 0\\ U & B \end{pmatrix}\) Λ = A 0 U B be a formal triangular matrix ring where A, B are rings and U is a (B, A)-bimodule. In this paper, we study some special classes over the formal triangular matrix ring \(\Lambda \) Λ . Further, using these special classes, we construct a left (resp. right) n-cotorsion pair over the formal triangular matrix ring \(\Lambda \) Λ from left (resp. right) n-cotorsion pairs over A and B. Finally, we give an example to illustrate our main results.