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<p>We study the commutativity of prime ring <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathfrak {R}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">R</mi> </math></EquationSource> </InlineEquation> on the action of permuting maps says, permuting <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\((\alpha ,\beta )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> <i>n</i>-derivations, and permuting generalized <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\((\alpha ,\beta )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> <i>n</i>-derivations. In this paper, we also generalized the result of Ashraf (Southeast Asian Bull. Math. 38:321–332, 2014),&#xa0;Theorem 2.6). Further, we also investigate some more results on the mentioned permuting maps with the help of traces.</p>

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Commutativity of Prime Ring with Permuting Generalized \((\alpha ,\beta )\) n-Derivation

  • 期刊论文

  • 发表日期：

    2025年7月14日

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  • Wasim Ahmed,
  • Muzibur Rahman Mozumder,
  • Adnan Abbasi

摘要

We study the commutativity of prime ring \(\mathfrak {R}\) R on the action of permuting maps says, permuting \((\alpha ,\beta )\) ( α , β ) n-derivations, and permuting generalized \((\alpha ,\beta )\) ( α , β ) n-derivations. In this paper, we also generalized the result of Ashraf (Southeast Asian Bull. Math. 38:321–332, 2014), Theorem 2.6). Further, we also investigate some more results on the mentioned permuting maps with the help of traces.