For an alternative <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_424_Article_IEq5.gif" Format="GIF" Height="9" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX"></EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-algebra A under some additional hypothesis, we prove that a map from A into itself is a nonlinear mixed <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_424_Article_IEq6.gif" Format="GIF" Height="9" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX"></EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-Jordan type derivation if and only is an additive <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_424_Article_IEq7.gif" Format="GIF" Height="9" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX"></EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-derivation. As consequence, some results on the complex octonion algebra, associative <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_424_Article_IEq8.gif" Format="GIF" Height="9" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX"></EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-algebras, and <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_424_Article_IEq9.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">$W^*$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>W</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-factor algebras were obtained.

About the additivity of a nonlinear mixed -Jordan type derivation defined on an alternative -algebra

期刊论文
发表日期：

2025年2月14日

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Tanise Carnieri Pierin,
Ruth Nascimento Ferreira,
Fernando Borges,
Bruno Leonardo Macedo Ferreira

摘要

For an alternative $*$ $*$ -algebra A under some additional hypothesis, we prove that a map from A into itself is a nonlinear mixed $*$ $*$ -Jordan type derivation if and only is an additive $*$ $*$ -derivation. As consequence, some results on the complex octonion algebra, associative $*$ $*$ -algebras, and $W^*$ $W^{*}$ -factor algebras were obtained.

About the additivity of a nonlinear mixed \(*\)-Jordan type derivation defined on an alternative \(*\)-algebra

摘要

About the additivity of a nonlinear mixed \(\)-Jordan type derivation defined on an alternative \(\)-algebra