Results 71 to 80 of about 3,309 (193)
Discrete Mathematics, 1992 A quasigroup \((Q,.,\setminus,/)\) is a set \(Q\) equipped with three binary operations \(.,\setminus,/\) such that (1) \((x/y).y = x\), \((x.y)/y = x\), (2) \(x.(x\setminus y) = y\), \(x\setminus(x.y) = y\). A right quasigroup \((Q,.,/)\) is a set \(Q\) with two binary operations \(.,/\) satisfying (1). A right quasigroup fulfilling \(x.x = x\) and \((
openaire +1 more source
An Algebraic Approach of Topological Indices Connected with Finite Quasigroups
Journal of Function Spaces, Volume 2024, Issue 1, 2024.In 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. The chemical reactivity of molecules, which includes their tendency to engage in particular chemical processes or go through particular reactions, can be ...
Muhammad Nadeem +4 more
wiley +1 more source
On groupoids with Bol-Moufang type identities [PDF]
Computer Science Journal of Moldova, 2020 We present results about groupoids of small order with Bol-Moufang type identities both classical and non-classical which are listed in [7], [9].
Grigorii Horosh +3 more
doaj
Global Left Loop Structures on Spheres [PDF]
, 2000 On the unit sphere $\mathbb{S}$ in a real Hilbert space $\mathbf{H}$, we derive a binary operation $\odot$ such that $(\mathbb{S},\odot)$ is a power-associative Kikkawa left loop with two-sided identity $\mathbf{e}_0$, i.e., it has the left inverse ...
Kinyon, Michael K.
core +1 more source
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
openaire +2 more sources
Graphs Connected to Isotopes of Inverse Property Quasigroups: A Few Applications
Journal of Applied Mathematics, Volume 2024, Issue 1, 2024.Many real‐world applications can be modelled as graphs or networks, including social networks and biological networks. The theory of algebraic combinatorics provides tools to analyze the functioning of these networks, and it also contributes to the understanding of complex systems and their dynamics.
Muhammad Nadeem +3 more
wiley +1 more source
On a special class of multivariate quadratic quasigroups (MQQs)
Journal of Mathematical Cryptology, 2013 In this paper, we study a special class of recently introduced quasigroups called multivariate quadratic quasigroups (MQQs) and solve several open research problems about them. Our main contributions are threefold. The first is to provide a standard form
Chen Yanling +2 more
doaj +1 more source
On recursively differentiable k-quasigroups [PDF]
, 2023 Parascovia Sirbu, Elena Cuznetov
openalex +1 more source
On free quasigroups and quasigroup representations
, 2018 This work consists of three parts. The discussion begins with \emph{linear quasigroups}. For a unital ring $S$, an $S$-linear quasigroup is a unital $S$-module, with automorphisms $\rho$ and $\lambda$ giving a (nonassociative) multiplication $x\cdot y=x^\rho+y^\lambda$. If $S$ is the field of complex numbers, then ordinary characters provide a complete
openaire +3 more sources