Selfdistributive Groupoids of Small Orders
نویسندگان
چکیده
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.
منابع مشابه
Selfdistributive Groupoids. Part A2: Non-idempotent Left Distributive Left Quasigroups
The present paper is a comprehensive survey of non-indempotent left distributive left quasigroups. It contains several new results about free groupoids and normal forms of terms in certain subvarieties. It is a continuation of a series of papers on selfdistributive groupoids, started by [KepN,03].
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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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My primary research interest is universal algebra. My thesis is about selfdistributive groupoids and their connection to other algebraic structures, such as groups and weakly associative loops. I am also interested ordered structures (residuated lattices in particular) and in the theory of quasigroups and loops. I am open to new interesting directions of research. A summary of my results follow...
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