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<p>We define a new type of product of hoops which, in the case of finite hoops, can decompose an arbitrary hoop <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textbf{A}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="bold">A</mi> </math></EquationSource> </InlineEquation> into a filter <i>F</i> and the corresponding homomorphic image <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\textbf{A}/F\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold">A</mi> <mo stretchy="false">/</mo> <mi>F</mi> </mrow> </math></EquationSource> </InlineEquation>. Since our new product is associative up to isomorphism, we can show that every finite hoop is representable as a product of finite MV-chains.</p>

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A New Representation of Finite Hoops Using a New Type of Product of Structures

  • 期刊论文

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  • 发表日期：

    2025年5月26日

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  • Michal Botur

摘要

We define a new type of product of hoops which, in the case of finite hoops, can decompose an arbitrary hoop \(\textbf{A}\) A into a filter F and the corresponding homomorphic image \(\textbf{A}/F\) A / F . Since our new product is associative up to isomorphism, we can show that every finite hoop is representable as a product of finite MV-chains.