Displaying similar documents to “Subdirectly irreducible non-idempotent left symmetric left distributive groupoids”

Quasitrivial left distributive groupoids

Robert El Bashir, Aleš Drápal (1994)

Commentationes Mathematicae Universitatis Carolinae

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Left distributive quasitrivial groupoids are completely described and those of them which are subdirectly irreducible are found. There are also determined all left distributive algebras A = A ( * , ∘ ) such that A ( * ) is a quasitrivial groupoid.

Selfdistributive groupoids of small orders

Jaroslav Ježek, Tomáš Kepka (1997)

Czechoslovak Mathematical Journal

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After enumerating isomorphism types of at most five-element left distributive groupoids, we prove that a distributive groupoid with less than 81 elements is necessarily medial.

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.