Results 1 to 10 of about 62 (60)
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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Right product quasigroups and loops
, 2009 15 pages; v2: minor corrections to author ...
Phillips, J D, Krapez, A, Kinyon, M K
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Journal of Algebra, 2016 A quantum quasigroup is a family \((A,\nabla,\Delta)\), where \((A,\nabla)\) is a magma in a given symmetric monoidal category, \((A,\Delta)\) is a comagma in the same category, such that the compositions \((\Delta\otimes 1_A)\circ(1_A\otimes\nabla)\) and \((1_A\otimes\Delta)(\nabla\otimes 1_A)\) are invertible.
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Integrally closed and complete ordered quasigroups and loops [PDF]
Proceedings of the American Mathematical Society, 1972 We generalize the well-known results on embedding a partially ordered group in its Dedekind extension by showing that, with the appropriate definition of integral closure, any partially ordered quasigroup (loop) G can be embedded in a complete partially ordered quasigroup (loop) if and only if G is integrally closed.
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Quasigroups, Loops, and Associative Laws
Journal of Algebra, 1996 The author investigates the question of which weakenings of the associative law imply that a quasigroup is a loop. In particular, he completely settles the question for all laws which are written with four variables, three of which are distinct (``size four laws''). In earlier work [J. Algebra 183, No.
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Quasigroups and Related Systems, 2023 This paper introduced a condition called $\mathcal{R}$-condition under which $(r,s,t)$-inverse quasigroups are universal. Middle isotopic $(r,s,t)$-inverse loops, satisfying the $\mathcal{R}$-condition and possessing a trivial set of $r$-weak inverse permutations were shown to be isomorphic; isotopy-isomorphy for $(r,s,t)$-inverse loops.
Richard Ilemobade +2 more
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One-Sided Quantum Quasigroups and Loops
Demonstratio Mathematica, 2015 AbstractQuantum 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. Just as quantum quasigroups are the “quantum” version of quasigroups, so one-sided quantum quasigroups are the “quantum ...
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Computing with small quasigroups and loops
, 2007 This is a companion to our lectures GAP and loops, to be delivered at the Workshops Loops 2007, Prague, Czech Republic. In the lectures we introduce the GAP package LOOPS, describe its capabilities, and explain in detail how to use it. In this paper we first outline the philosophy behind the package and its main features, and then we focus on three ...
Nagy, G.P., Vojtĕchovský, P.
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