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<p>We present an example that the usual natural extension of a generalized effect algebra to an effect algebra need not preserve infinite suprema, i.e., the original generalized effect algebra need not be a (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>-)complete order ideal in the extension.</p>

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A Note on Extensions of Generalized Effect Algebras to Effect Algebras

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月12日

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  • Josef Tkadlec

摘要

We present an example that the usual natural extension of a generalized effect algebra to an effect algebra need not preserve infinite suprema, i.e., the original generalized effect algebra need not be a ( \(\sigma \) σ -)complete order ideal in the extension.