<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\mathcal {R}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">R</mi> </math></EquationSource> </InlineEquation> be a nonzero prime ring with characteristic other than 2 and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathcal {L}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">L</mi> </math></EquationSource> </InlineEquation> be a non central Lie ideal of ring <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\mathcal {R}.$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">R</mi> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> Assume that <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\mathcal {T}_1$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">T</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\mathcal {T}_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">T</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> are <i>b</i>-generalized skew derivations on <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\mathcal {R}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">R</mi> </math></EquationSource> </InlineEquation> such that <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$p\Big (\mathcal {T}_1(x)x-x\mathcal {T}_2(x)\Big )=0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mrow> <mo maxsize="1.623em" minsize="1.623em" stretchy="true">(</mo> </mrow> <msub> <mi mathvariant="script">T</mi> <mn>1</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mi>x</mi> <mo>-</mo> <mi>x</mi> <msub> <mi mathvariant="script">T</mi> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mo maxsize="1.623em" minsize="1.623em" stretchy="true">)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> for all <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$x \in \mathcal {L}.$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>x</mi> <mo>∈</mo> <mi mathvariant="script">L</mi> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> We examine complete possible structures of <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$\mathcal {T}_1$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">T</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$\mathcal {T}_2.$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">T</mi> <mn>2</mn> </msub> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> This extends the result of Rania [19. Communications in Algebra]</p>

Actions of annihilating b-generalized skew derivations on Lie ideals

期刊论文
发表日期：

2026年6月29日

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Pallavee Gupta,
S. K. Tiwari,
Vincenzo De Filippis

摘要

Let $\mathcal {R}$ $R$ be a nonzero prime ring with characteristic other than 2 and $\mathcal {L}$ $L$ be a non central Lie ideal of ring $\mathcal {R}.$ $R .$ Assume that $\mathcal {T}_1$ $T_{1}$ and $\mathcal {T}_2$ $T_{2}$ are b-generalized skew derivations on $\mathcal {R}$ $R$ such that $p\Big (\mathcal {T}_1(x)x-x\mathcal {T}_2(x)\Big )=0$ $p (T_{1} (x) x - x T_{2} (x)) = 0$ for all $x \in \mathcal {L}.$ $x \in L .$ We examine complete possible structures of $\mathcal {T}_1$ $T_{1}$ and $\mathcal {T}_2.$ $T_{2} .$ This extends the result of Rania [19. Communications in Algebra]