Scholarlink

<p>The results concern Ore ring extensions, including differential and skew polynomial extensions, with particular emphasis on the prime radical <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\beta \)</EquationSource> </InlineEquation>. It is shown that for an algebra <i>R</i> over a field with a locally algebraic endomorphism <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\beta (R) \subseteq \beta (R[x; \sigma ])\)</EquationSource> </InlineEquation>. An analogous result is obtained for algebras of the form <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(R[x; \delta ]\)</EquationSource> </InlineEquation> with a locally algebraic derivation <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\delta \)</EquationSource> </InlineEquation>, provided that the prime radical <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\beta (R)\)</EquationSource> </InlineEquation> is <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\delta \)</EquationSource> </InlineEquation>-stable.</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

On prime radical of ore extensions

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年6月22日

查看全文
  • Marek Kȩpczyk

摘要

The results concern Ore ring extensions, including differential and skew polynomial extensions, with particular emphasis on the prime radical \(\beta \) . It is shown that for an algebra R over a field with a locally algebraic endomorphism \(\sigma \) , \(\beta (R) \subseteq \beta (R[x; \sigma ])\) . An analogous result is obtained for algebras of the form \(R[x; \delta ]\) with a locally algebraic derivation \(\delta \) , provided that the prime radical \(\beta (R)\) is \(\delta \) -stable.