Results 41 to 50 of about 1,878 (148)
Parastrophe of Some Inverse Properties in Quasigroups
MathematicsThis work investigates the relationship between the parastrophes of some notion of inverses in quasigroups. Our findings reveal that, of the 5 parastrophes of LIP quasigroup, (23) parastrophe is a LIP quasigroup, (12) and (132) parastrophes are RIP ...
Yakub T. Oyebo +3 more
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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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Pseudococyclic Partial Hadamard Matrices over Latin Rectangles
Mathematics, 2021 The classical design of cocyclic Hadamard matrices has recently been generalized by means of both the notions of the cocycle of Hadamard matrices over Latin rectangles and the pseudococycle of Hadamard matrices over quasigroups.
Raúl M. Falcón +4 more
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Half quasigroups and generalized quasigroup orthogonality
Discrete Mathematics, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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How Nonassociative Geometry Describes a Discrete Spacetime
Frontiers in Physics, 2019 Nonassociative geometry, providing a unified description of discrete and continuum spaces, is a valuable candidate for the study of discrete models of spacetime. Within the framework of nonassociative geometry we propose a model of emergent spacetime. In
Alexander I. Nesterov, Héctor Mata
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Mathematica Slovaca, 2011 Abstract Napoleon’s quasigroups are idempotent medial quasigroups satisfying the identity (ab·b)(b·ba) = b. In works by V. Volenec geometric terminology has been introduced in medial quasigroups, enabling proofs of many theorems of plane geometry to be carried out by formal calculations in a quasigroup.
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Subsystems and Automorphisms of Some Finite Magmas of Order k + k2 [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2020 This work is devoted to the study of subsystems of some finite magmas S = (V,*) with a generating set of k elements and order k + k2. For k more than 1, the magmas S are not semigroups and quasigroups.
Litavrin, Andrey Viktorovich
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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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