Scholarlink

<p>Let <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1299_Article_IEq7.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {M}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">M</mi> </math></EquationSource> </InlineEquation> be a unital prime complex <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1299_Article_IEq1.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 having a non-trivial projection. In this paper, we proved that every <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1299_Article_IEq1.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-type map <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1299_Article_IEq10.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="98" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Phi :\mathcal {M}\rightarrow \mathcal {M}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Φ</mi> <mo>:</mo> <mi mathvariant="script">M</mi> <mo stretchy="false">→</mo> <mi mathvariant="script">M</mi> </mrow> </math></EquationSource> </InlineEquation> on sum of triple products <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1299_Article_IEq11.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="388" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha _{1} abc+\alpha _{2} a^{*}cb^{*}+\alpha _{3} bac +\alpha _{4} ca^{*}b^{*}+\alpha _{5} bca+\alpha _{6} cb^{*}a^{*},\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>α</mi> <mn>1</mn> </msub> <mi>a</mi> <mi>b</mi> <mi>c</mi> <mo>+</mo> <msub> <mi>α</mi> <mn>2</mn> </msub> <mmultiscripts> <mi>a</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> <mi>c</mi> <mmultiscripts> <mi>b</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> <mo>+</mo> <msub> <mi>α</mi> <mn>3</mn> </msub> <mi>b</mi> <mi>a</mi> <mi>c</mi> <mo>+</mo> <msub> <mi>α</mi> <mn>4</mn> </msub> <mi>c</mi> <mmultiscripts> <mi>a</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> <mmultiscripts> <mi>b</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> <mo>+</mo> <msub> <mi>α</mi> <mn>5</mn> </msub> <mi>b</mi> <mi>c</mi> <mi>a</mi> <mo>+</mo> <msub> <mi>α</mi> <mn>6</mn> </msub> <mi>c</mi> <mmultiscripts> <mi>b</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> <mmultiscripts> <mi>a</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> where the scalars <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1299_Article_IEq12.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">\(\{\alpha _{k}\}_{k=1}^{6}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mrow> <mo stretchy="false">{</mo> <msub> <mi>α</mi> <mi>k</mi> </msub> <mo stretchy="false">}</mo> </mrow> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>6</mn> </msubsup> </math></EquationSource> </InlineEquation> are rational numbers satisfying some conditions, is an additive <InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1299_Article_IEq1.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. An application of the main result is also presented.</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

Maps of \(*\)-derivation-type on sums of triple products on \(*\)-algebras

  • 期刊论文

  • 发表日期：

    2025年4月7日

查看全文
  • João Carlos da Motta Ferreira,
  • Maria das Graças Bruno Marietto

摘要

Let \(\mathcal {M}\) M be a unital prime complex \(*\) ∗ -algebra having a non-trivial projection. In this paper, we proved that every \(*\) ∗ -derivation-type map \(\Phi :\mathcal {M}\rightarrow \mathcal {M}\) Φ : M → M on sum of triple products \(\alpha _{1} abc+\alpha _{2} a^{*}cb^{*}+\alpha _{3} bac +\alpha _{4} ca^{*}b^{*}+\alpha _{5} bca+\alpha _{6} cb^{*}a^{*},\) α 1 a b c + α 2 a ∗ c b ∗ + α 3 b a c + α 4 c a ∗ b ∗ + α 5 b c a + α 6 c b ∗ a ∗ , where the scalars \(\{\alpha _{k}\}_{k=1}^{6}\) { α k } k = 1 6 are rational numbers satisfying some conditions, is an additive \(*\) ∗ -derivation. An application of the main result is also presented.