Results 21 to 30 of about 1,056 (96)
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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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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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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Topology of quasi divisor graphs associated with non-associative algebra
Ain Shams Engineering JournalThe visualization of graphs representing algebraic structures has increasingly gained traction in chemical engineering research, emerging as a significant scientific challenge in contemporary studies.
Muhammad Nadeem +4 more
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Distributive and trimedial quasigroups of order 243
, 2016 We enumerate three classes of non-medial quasigroups of order $243=3^5$ up to isomorphism. There are $17004$ non-medial trimedial quasigroups of order $243$ (extending the work of Kepka, B\'en\'eteau and Lacaze), $92$ non-medial distributive quasigroups ...
Jedlička, Přemysl +2 more
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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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Commuting Pairs in Quasigroups
Journal of Combinatorial Designs, Volume 33, Issue 11, Page 418-427, November 2025.ABSTRACT A quasigroup is a pair ( Q , ∗ ), where Q is a nonempty set and ∗ is a binary operation on Q such that for every ( a , b ) ∈ Q 2, there exists a unique ( x , y ) ∈ Q 2 such that a ∗ x = b = y ∗ a. Let ( Q , ∗ ) be a quasigroup. A pair ( x , y ) ∈ Q 2 is a commuting pair of ( Q , ∗ ) if x ∗ y = y ∗ x.
Jack Allsop, Ian M. Wanless
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On a “grouplike” family of quasigroups
Examples and CounterexamplesQuasigroups are algebraic structures in which divisibility is always defined. This paper illustrates some similarities and differences between quasigroup theory and group theory, by singling out a special family of quasigroups which seem to be most ...
Ahmed Al Fares, Gizem Karaali
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