Results 81 to 90 of about 166 (137)
The Burnside algebra of a quasigroup
Journal of Algebra, 2004 In this paper the author extends the Burnside algebra concept from groups to quasigroups. Given a subquasigroup \(P\) of a finite quasigroup \(Q\), the elements of the corresponding homogeneous space \(P\setminus Q\) are the orbits on \(Q\) of the relative left multiplication group of \(P\) in \(Q\).
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Asian Journal of Mathematics, 2016 In this paper we introduce the notion of weak Hopf quasigroup as a generalization of weak Hopf algebras and Hopf quasigroups. We obtain its main properties and we prove the fundamental theorem of Hopf modules for these algebraic structures.
Álvarez, J. N. Alonso +2 more
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About International Conference MITI2018 [PDF]
Computer Science Journal of Moldova, 2018 The conference is a homage to the illustrious mathematician Valentin Belousov, the founder of the Theory of Quasigroups and Loops in the former USSR, doctor habilitate in physics and mathematics, professor, correspondent member at the Academy of ...
Ina Ciobanu +2 more
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Algebraic Properties of Quasigroup Under Q-neutrosophic Soft Set [PDF]
Neutrosophic Sets and SystemsThe novel concept called neutrosophic set was launched to take care of indeterminate factors in real-life data. The hybrid model of neutrosophic set and soft set has been widely studied in different areas of algebra, especially in associative structures ...
Benard Osoba +2 more
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Quasigroups, right quasigroups, coverings and representations
, 2018 For a fixed quasigroup Q, equivalences are established between the following categories: (i) the category of modules over the quasigroup; (ii) the category of representations of a stabilizer in the universal multiplication group; (iii) the category of representations of the fundamental groupoid of the Cayley diagram of the quasigroup in the category of
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Note on Quasigroups and Trees [PDF]
Proceedings of the Edinburgh Mathematical Society, 1963 If letters a, b, c, … are used to denote points of a nondegenerate plane cubic curve, other than the singular point if any, and if the product ab is defined as the third point of the curve collinear with a and b, we obtain an algebraic system having nonassociative multiplication (ab . c ≠ a . bc in general).
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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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Isotopy and parastrophy of quasigroups [PDF]
Proceedings of the American Mathematical Society, 1963 1. It has been noted that every quasigroup (Q, *) belongs to a set of 6 quasigroups, called adjugate by Fisher and Yates [4], conjugate by Stein [6], parastrophic by Sade [5]. If in (Q, *), xy=z, then in the parastrophic quasigroups (xx) (x) (yx) = zw, where wr is one of the 6 permutations of {x, yy,Z }, v7r the image of vI{xI y, Z } under wx, and (wx)
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Varieties of Hexagonal Quasigroups
Journal of Algebra, 1993 The decomposition of a complete graph into disjoint cycles can be used to define a binary operation \(\star\) on the vertices of the graph -- if a cycle is \((\dots, a, b, c, \dots)\) then \(a \star b = c\) and \(c \star b = a\). In general the groupoid thus obtained is not a quasigroup, but when the decomposition satisfies an extra condition, known as
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Quasigroups, Braided Hopf (Co)quasigroups and Radford’s Biproducts of Quasi-Diagonal Type
MathematicsGiven the Yetter–Drinfeld category over any quasigroup and a braided Hopf coquasigroup in this category, we first mainly study the Radford’s biproduct corresponding to this braided Hopf coquasigroup.
Yue Gu, Shuanhong Wang
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