Results 51 to 60 of about 166 (137)
Yetter–Drinfeld Modules for Group-Cograded Hopf Quasigroups
Mathematics, 2022 Let H be a crossed group-cograded Hopf quasigroup. We first introduce the notion of p-Yetter–Drinfeld quasimodule over H. If the antipode of H is bijective, we show that the category YDQ(H) of Yetter–Drinfeld quasimodules over H is a crossed category ...
Huili Liu, Tao Yang, Lingli Zhu
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Discrete Mathematics, 1992 A quasigroup \((Q,.,\setminus,/)\) is a set \(Q\) equipped with three binary operations \(.,\setminus,/\) such that (1) \((x/y).y = x\), \((x.y)/y = x\), (2) \(x.(x\setminus y) = y\), \(x\setminus(x.y) = y\). A right quasigroup \((Q,.,/)\) is a set \(Q\) with two binary operations \(.,/\) satisfying (1). A right quasigroup fulfilling \(x.x = x\) and \((
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Inverse Spectrum and Structure of Topological Metagroups
MathematicsIn this article, a structure of topological metagroups is scrutinized. Their inverse spectra are studied. This also permits us to construct abundant families of topological metagroups and quasigroups.
Sergey Victor Ludkowski
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Quasigroups in cryptology [PDF]
Computer Science Journal of Moldova, 2009 We give a review of some known published applications of quasigroups in cryptology.
V.A. Shcherbacov
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Quasigroups and related systems, 2010 In this paper the concept of ARO-quasigroup is introduced and some identities which are valid in a general ARO-quasigroup are proved. The "geometric" concepts of midpoint, parallelogram and affine-regular octagon is introduced in a general ARO-quasigroup.
Kolar-Šuper, Ružica +2 more
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Journal of Algebra, 1996 It is well known that the following four Moufang identities, M1: \((x(yz))x=(xy)(zx)\) and N1: \(((xy)z)y=x(y(zy))\) and their respective mirrors M2 and N2 (obtained by writing them backwards), are equivalent in loops which are then called Moufang loops. The author now shows that every quasigroup satisfying any one of these four identities is a Moufang
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Row‐Hamiltonian Latin squares and Falconer varieties
Proceedings of the London Mathematical Society, Volume 128, Issue 1, January 2024.Abstract A Latin square is a matrix of symbols such that each symbol occurs exactly once in each row and column. A Latin square L$L$ is row‐Hamiltonian if the permutation induced by each pair of distinct rows of L$L$ is a full cycle permutation. Row‐Hamiltonian Latin squares are equivalent to perfect 1‐factorisations of complete bipartite graphs.
Jack Allsop, Ian M. Wanless
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Finite automata over magmas: models and some applications in Cryptography [PDF]
Computer Science Journal of Moldova, 2018 In the paper the families of finite semi-automata and reversible finite Mealy and Moore automata over finite magmas are defined and analyzed in detail.
Volodymyr V. Skobelev +1 more
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Quasigroups and related systems, 2009 The concept of a LGS-quasigroup is defined and investigated in this paper. The geometric concepts of parallelograms and midpoints are introduced in a general LGS-quasigroup and the geometrical interpretation in the LGS-quasigroup $C(\frac{;1};{;2};(3 + \sqrt 5))$ is given.
Kolar Begović, Zdenka +1 more
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Graphs Connected to Isotopes of Inverse Property Quasigroups: A Few Applications
Journal of Applied Mathematics, Volume 2024, Issue 1, 2024.Many real‐world applications can be modelled as graphs or networks, including social networks and biological networks. The theory of algebraic combinatorics provides tools to analyze the functioning of these networks, and it also contributes to the understanding of complex systems and their dynamics.
Muhammad Nadeem +3 more
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