Enumerating left distributive groupoids

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Enumerating Left Distributive Groupoids

Groupoids satisfying the equation x(yz) = (xy)(xz) are called left distributive, or LD-groupoids. We give an algorithm for their enumeration and prove several results on the collection of LD-groupoids extending a given monounary algebra.

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Selfdistributive groupoids Part D1: Left distributive semigroups

Every semilattice (i.e., an idempotent commutative semigroup) is selfdistributive. An explicit formulation of this fact (perhaps for the first time) can be found already in C. S. Pierce [Pie,80]. A structural study of two-sided selfdistributive semigroups was initiated in M. Petrich [Pet,69] and that of one-sided selfdistributive semigroups ten years later in S. Markovski [Mar,79]. Altogether, ...

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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 x ≈ x decomposes as the direct product of its largest idempotent factor and a ...

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ژورنال

عنوان ژورنال: Czechoslovak Mathematical Journal

سال: 1997

ISSN: 0011-4642,1572-9141

DOI: 10.1023/a:1022826819995