Results 11 to 20 of about 67 (63)
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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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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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 ...
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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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An Algebraic Approach of Topological Indices Connected with Finite Quasigroups
Journal of Function SpacesIn mathematical chemistry, the algebraic polynomial serves as essential for calculating the most accurate expressions of distance-based, degree-distance-based, and degree-based topological indices.
Muhammad Nadeem +3 more
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SAC loops and loops of order five
Математика, інформатика, фізика: наука та освітаIn this article, we continue the analytical research of small-order loops. Namely, we investigate loops of order 5. Recall that an element of a loop is called unipotent if its square is neutral.
Fedir Sokhatsky
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Computing with small quasigroups and loops
, 2015 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, Gábor P., Vojtěchovský, Petr
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Linking Bipartiteness and Inversion in Algebra via Graph-Theoretic Methods and Simulink
ComplexityResearch for decades has concentrated on graphs of algebraic structures, which integrate algebra and combinatorics in an innovative way. The goal of this study is to characterize specific aspects of bipartite and inverse graphs that are associated with ...
Mohammad Mazyad Hazzazi +5 more
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Lattice-ordered loops and quasigroups
Journal of Algebra, 1970 AbstractIn studying the effect of an order on non-associative systems such as loops or quasigroups, a natural question to ask is whether some order condition which implies commutativity in the group case implies associativity in the corresponding loop case.
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