Results 31 to 40 of about 160,139 (111)
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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, 2022 We will begin by discussing power graphs of Moufang loops. We are able to show that as in groups the directed power graph of a Moufang loop is uniquely determined by the undirected power graph.
Britten, Riley
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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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On congruences and ideals of partially ordered quasigroups [PDF]
, 2008 summary:Some results concerning congruence relations on partially ordered quasigroups (especially, Riesz quasigroups) and ideals of partially ordered loops are presented.
Demko, Milan
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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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Journal of Mathematics, Volume 2026, Issue 1, 2026.A connection between cryptography and polynomial functions is extremely significant. Mathematical performance of polynomials helps to enhance the cryptographic primitives, which are trustworthy as well as straightforward representation tools, in everyday use. In this research, explicit topological sequences Qf which correspond to degree‐based, distance‐
Mohammad Mazyad Hazzazi +5 more
wiley +1 more source
, 2002 The theory of loops (groups without associativity), though researched by several mathematicians has not found a sound expression, for books, be it research level or otherwise, solely dealing with the properties of loops are absent.
VASANTHA, KANDASAMY
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Topological Aspects of Quadratic Graphs and M‐Polynomials Utilizing Classes of Finite Quasigroups
Journal of Mathematics, Volume 2026, Issue 1, 2026.Material science, drug design and toxicology studies, which relate a molecule’s structure to its numerous properties and activities, are studied with the use of the topological index. Graphs with finite algebraic structure find extensive applications in fields such as mathematics, elliptic curve cryptography, physics, robotics and information theory ...
Mohammad Mazyad Hazzazi +5 more
wiley +1 more source
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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Canonical Labeling of Latin Squares in Average‐Case Polynomial Time
Random Structures &Algorithms, Volume 66, Issue 4, July 2025.ABSTRACT A Latin square of order n$$ n $$ is an n×n$$ n\times n $$ matrix in which each row and column contains each of n$$ n $$ symbols exactly once. For ε>0$$ \varepsilon >0 $$, we show that with high probability a uniformly random Latin square of order n$$ n $$ has no proper subsquare of order larger than n1/2log1/2+εn$$ {n}^{1/2}{\log}^{1/2 ...
Michael J. Gill +2 more
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