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<p>We provide a classification for the class of unilinear residuated lattices (URLs) into four natural subclasses. We give axiomatizations for each class and for the varieties they generate. We further produce constructions that show that algebras of each class can be obtained from <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\top \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>⊤</mi> </math></EquationSource> </InlineEquation>-unital URLs (one of the four classes); this reduces the study of all URLs to the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\top \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>⊤</mi> </math></EquationSource> </InlineEquation>-unital ones, already studied in previous work. Finally we show how class operators interact with the constructions and provide descriptions of the subvariety lattices.</p>

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Classification of unilinear residuated lattices

  • 期刊论文

  • 发表日期：

    2026年4月21日

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  • Nikolaos Galatos,
  • Xiao Zhuang

摘要

We provide a classification for the class of unilinear residuated lattices (URLs) into four natural subclasses. We give axiomatizations for each class and for the varieties they generate. We further produce constructions that show that algebras of each class can be obtained from \(\top \) ⊤ -unital URLs (one of the four classes); this reduces the study of all URLs to the \(\top \) ⊤ -unital ones, already studied in previous work. Finally we show how class operators interact with the constructions and provide descriptions of the subvariety lattices.