Hamiltonian selfdistributive quasigroups
نویسندگان
چکیده
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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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.
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The category of modules over a fixed quasigroup in the category of all quasigroups is equivalent to the category of representations of the fundamental groupoid of the Cayley diagram of the quasigroup in the category of abelian groups. The corresponding equivalent category of coverings, and the generalization to the right quasigroup case, are also described.
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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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Decompositions of complete undirected graphs into sets of closed trails which partition the edge set of the graph and which contain each pair of distinct vertices exactly once at distance 2 define and are defined by a class of quasigroups called P-quasigroups. Conditions are established under which P-quasigroups are (or are not) homomorphic images of P-quasigroups which possess certain properti...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2005
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2005.03.017