Some remarks on distributive groupoids
Józef Dudek (1981)
Czechoslovak Mathematical Journal
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Józef Dudek (1981)
Czechoslovak Mathematical Journal
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Aleš Drápal, Tomáš Kepka, Michal Musílek (1994)
Commentationes Mathematicae Universitatis Carolinae
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We show that group conjugation generates a proper subvariety of left distributive idempotent groupoids. This subvariety coincides with the variety generated by all cancellative left distributive groupoids.
J. Dudek (1970)
Colloquium Mathematicae
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J. Dudek (1984)
Fundamenta Mathematicae
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David Stanovský (2011)
Acta Universitatis Carolinae. Mathematica et Physica
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David Stanovský (2004)
Discussiones Mathematicae - General Algebra and Applications
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We describe a part of the lattice of subvarieties of left distributive left idempotent groupoids (i.e. those satisfying the identities x(yz) ≈ (xy)(xz) and (xx)y ≈ xy) modulo the lattice of subvarieties of left distributive idempotent groupoids. A free groupoid in a subvariety of LDLI groupoids satisfying an identity xⁿ ≈ x decomposes as the direct product of its largest idempotent factor and a cycle. Some properties of subdirectly ireducible LDLI groupoids are found.
J. Dudek (1976)
Colloquium Mathematicae
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