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<p>The essential aim of this article is to introduce the definitions concerning a <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\((\sigma , \tau )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>σ</mi> <mo>,</mo> <mi>τ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-homoderivation (resp. a <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\((\sigma , \tau )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>σ</mi> <mo>,</mo> <mi>τ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-antihomoderivation) and homogeneralized <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\((\sigma ,\tau )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>σ</mi> <mo>,</mo> <mi>τ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-derivations (resp. a antihomogeneralized <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\((\sigma ,\tau )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>σ</mi> <mo>,</mo> <mi>τ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-derivation) of a ring where <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation> are many-to-one functions over <i>R</i>. In doing so, we present a number of various results that can be either deduced or generalized that gain strength when examined as a contribution to the theory of homoderivations on prime rings and semiprime rings.</p>

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Homogeneralized \((\sigma ,\tau )\)-derivations of Associative Rings

  • 期刊论文

  • 发表日期：

    2025年8月16日

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  • Mehsin Jabel Atteya

摘要

The essential aim of this article is to introduce the definitions concerning a \((\sigma , \tau )\) ( σ , τ ) -homoderivation (resp. a \((\sigma , \tau )\) ( σ , τ ) -antihomoderivation) and homogeneralized \((\sigma ,\tau )\) ( σ , τ ) -derivations (resp. a antihomogeneralized \((\sigma ,\tau )\) ( σ , τ ) -derivation) of a ring where \(\sigma \) σ and \(\tau \) τ are many-to-one functions over R. In doing so, we present a number of various results that can be either deduced or generalized that gain strength when examined as a contribution to the theory of homoderivations on prime rings and semiprime rings.