Displaying similar documents to “Two-generated idempotent groupoids with small clones”

Group conjugation has non-trivial LD-identities

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.

On varieties of left distributive left idempotent groupoids

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.