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<p>By studying self-majorizing elements, we provide a comprehensive description of finite elements within Archimedean <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\phi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϕ</mi> </math></EquationSource> </InlineEquation>-algebras. Our investigation yields various algebraic and topological characterizations of these elements. As an application, a necessary and sufficient condition for which <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(Orth(A)=Z(A)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mi>r</mi> <mi>t</mi> <mi>h</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>Z</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> holds, where <i>A</i> is an Archimedean vector lattice.</p>

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Finite elements in Archimedean \(\Phi \)-algebras

  • 期刊论文

  • 发表日期：

    2025年9月18日

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  • Zied Jbeli,
  • Mohamed Ali Toumi,
  • Nedra Toumi

摘要

By studying self-majorizing elements, we provide a comprehensive description of finite elements within Archimedean \(\phi \) ϕ -algebras. Our investigation yields various algebraic and topological characterizations of these elements. As an application, a necessary and sufficient condition for which \(Orth(A)=Z(A)\) O r t h ( A ) = Z ( A ) holds, where A is an Archimedean vector lattice.