Results 1 to 10 of about 1,017 (59)
One-Sided Quantum Quasigroups and Loops
Demonstratio Mathematica, 2015 Quantum quasigroups and quantum loops are self-dual objects providing a general framework for the nonassociative extension of quantum group techniques. This paper examines their one-sided analogues, which are not self-dual.
Smith J. D. H.
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A Pair of Smarandachely Isotopic Quasigroups and Loops of the Same Variety [PDF]
, 2008 The isotopic invariance or universality of types and varieties of quasigroups and loops described by one or more equivalent identities has been of interest to researchers in loop theory in the recent past.
Jaiyeola, Temitope Gbolahan
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Topologies on Smashed Twisted Wreath Products of Metagroups
Axioms, 2023 In this article, topologies on metagroups and quasigroups are studied. Topologies on smashed twisted wreath products of metagroups are scrutinized, which are making them topological metagroups. For this purpose, transversal sets are studied.
Sergey Victor Ludkowski
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Rectangular quasigroups and rectangular loops
Computers & Mathematics with Applications, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kinyon, M.K., Phillips, J.D.
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Principal Loop-Isotopes of Quasigroups [PDF]
Canadian Journal of Mathematics, 1966 If a quasigroup (L, .) has finite order n, then there are n2 principal loop-isotopes. Some of these n2 loops may be isomorphic, and the main purpose of this paper is to obtain theorems that describe the isomorphism classes. Using these results and a computer, we have determined all the loops of order 6.
Bryant, B. F., Schneider, H.
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Small latin squares, quasigroups, and loops [PDF]
Journal of Combinatorial Designs, 2006 AbstractWe present the numbers of isotopy classes and main classes of Latin squares, and the numbers of isomorphism classes of quasigroups and loops, up to order 10. The best previous results were for Latin squares of order 8 (Kolesova, Lam, and Thiel,1990), quasigroups of order 6 (Bower,2000), and loops of order 7 (Brant and Mullen,1985). The loops of
McKay, Brendan +2 more
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On the number of n-ary quasigroups of finite order [PDF]
, 2012 Let $Q(n,k)$ be the number of $n$-ary quasigroups of order $k$. We derive a recurrent formula for Q(n,4). We prove that for all $n\geq 2$ and $k\geq 5$ the following inequalities hold: $({k-3}/2)^{n/2}(\frac{k-1}2)^{n/2} < log_2 Q(n,k) \leq {c_k(k-2)^{n}}
Krotov, Denis, Potapov, Vladimir
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Parastrophic invariance of Smarandache quasigroups [PDF]
, 2006 The study of the Smarandache concept in groupoids was initiated by W.B. Vasantha Kandasamy in [18]. In her book and first paper on Smarandache concept in loops, she defined a Smarandache loop as a loop with at least a subloop which forms a subgroup ...
Gbolahan, Temitope
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On the universality of some Smarandache loops of Bol-Moufang type [PDF]
, 2006 A Smarandache left (right) inverse property loop in which all its f; g- principal isotopes are Smarandache f; g- principal isotopes is shown to be universal if and only if it is a Smarandache left(right) Bol loop in which all its f; g- principal isotopes
Awolowo, Obafemi +1 more
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How Nonassociative Geometry Describes a Discrete Spacetime
Frontiers in Physics, 2019 Nonassociative geometry, providing a unified description of discrete and continuum spaces, is a valuable candidate for the study of discrete models of spacetime. Within the framework of nonassociative geometry we propose a model of emergent spacetime. In
Alexander I. Nesterov, Héctor Mata
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