Abstract
To any bounded lattice with section antitone bijections can be assigned an algebra with two binary, two unary and a nullary operations satisfying similar axioms as a basic algebra. Due to the doubled similarity type, this algebra is called a double basic algebra. Also conversely, every double basic algebra induces a bounded lattice equipped with antitone bijections in every section. We study properties of double basic algebras, their interval algebras and several conclusions of the so-called pseudo-commutativity.
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This work is supported by the Research Project MSM 6198959214 by Czech Government.
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Chajda, I. Double Basic Algebras. Order 26, 149–162 (2009). https://doi.org/10.1007/s11083-009-9113-0
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DOI: https://doi.org/10.1007/s11083-009-9113-0