Displaying similar documents to “On some finite groupoids with distributive subgroupoid lattices”

Meet-distributive lattices have the intersection property

Henri Mühle (2023)

Mathematica Bohemica

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This paper is an erratum of H. Mühle: Distributive lattices have the intersection property, Math. Bohem. (2021). Meet-distributive lattices form an intriguing class of lattices, because they are precisely the lattices obtainable from a closure operator with the so-called anti-exchange property. Moreover, meet-distributive lattices are join semidistributive. Therefore, they admit two natural secondary structures: the core label order is an alternative order on the lattice elements and...

Distributive lattices with a given skeleton

Joanna Grygiel (2004)

Discussiones Mathematicae - General Algebra and Applications

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We present a construction of finite distributive lattices with a given skeleton. In the case of an H-irreducible skeleton K the construction provides all finite distributive lattices based on K, in particular the minimal one.

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.

Ideals in selfdistributive groupoids

Tomáš Kepka (1994)

Commentationes Mathematicae Universitatis Carolinae

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Products of (left) ideals in selfdistributive groupoids are studied.

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.