Results 11 to 20 of about 2,856 (140)

Okubo quasigroups

Documenta Mathematica, 2022
Paige loops, simple non-associative Moufang loops, were constructed by Paige as quotients of the set of Zorn vector-matrices of unit norm under split octonion multiplication. In this paper, we show that the same quotient set sustains two related simple quasigroup structures, in which the split octonion multiplication is replaced with multiplication ...
Smith, Jonathan D. H., Vojtěchovský, Petr   +1 more
openaire   +2 more sources

Identities and generalized derivatives of quasigroups [PDF]

Computer Science Journal of Moldova, 2022
We associate a partial (autostrophical) identity with every generalized derivative. We research when a quasigroup that satisfies an autostrophic identity has a unit (left or/and right or/and middle).
G. Horosh, N. Malyutina, A. Scerbacova, V. Shcherbacov   +3 more
doaj   +1 more source

Parastrophic invariance of Smarandache quasigroups [PDF]

, 2006
The study of the Smarandache concept in groupoids was initiated by W.B. Vasantha Kandasamy in [18]. In her book and first paper on Smarandache concept in loops, she defined a Smarandache loop as a loop with at least a subloop which forms a subgroup ...
Gbolahan, Temitope
core   +1 more source

Isotopic Properties of Neutrosophic Soft Quasigroup and Its Application in Decision-making [PDF]

Neutrosophic Sets and Systems
A Q-neutrosophic soft quasigroup (ϕ Q, A) represents a novel mathematical framework designed to address scenarios characterized by indeterminate occurrences.
Benard Osoba, Oyebo Tunde Yakub, Abdulkareem Abdulafeez Olalekan, Oyewole Oluwapamilerin, Adenibuyan Micheal Tokunbo, Oluwatobi Balogun, Adekola Lanrewaju Olumide   +6 more
doaj   +1 more source

Medial quasigroups of prime square order [PDF]

, 2016
We prove that, for any prime $p$, there are precisely $2p^4-p^3-p^2-3p-1$ medial quasigroups of order $p^2$, up to ...
Stanovský, David
core   +2 more sources

Study of Jordan quasigroups and their construction

Journal of Taibah University for Science, 2018
Jordan quasigroups are commutative quasigroups satisfying the identity $x^{2}(yx)=(x^{2}y)x$. In this paper we discuss the basic properties of Jordan quasigroups and prove that (i) every commutative idempotent quasigroup is Jordan quasigroup, (ii) if a ...
Amir Khan, Muhammad Shah, Hidayat Ullah Khan, Gul Zaman   +3 more
doaj   +1 more source

Rota–Baxter (Co)algebra Equation Systems and Rota–Baxter Hopf Algebras

Mathematics, 2022
We introduce and discuss the notions of Rota–Baxter bialgebra equation systems and Rota–Baxter Hopf algebras. Then we construct a lot of examples based on Hopf quasigroups.
Yue Gu, Shuanhong Wang, Tianshui Ma
doaj   +1 more source

Distributive Properties of Q−neutrosophic Soft Quasigroups [PDF]

Neutrosophic Sets and Systems, 2023
The Q−neutrosophic soft quasigroup is a mathematical innovation for dealing with indeterminate occurrences. The characterization of quasigroups using the concept of Q−neutrosophic soft set is an evolving area of study that, in recent times, has attracted
Oyobo Tunde Yakub, Benard Osoba, Abdulkareem Abdulafeez Olalekan   +2 more
doaj   +1 more source

On the number of n-ary quasigroups of finite order [PDF]

, 2012
Let $Q(n,k)$ be the number of $n$-ary quasigroups of order $k$. We derive a recurrent formula for Q(n,4). We prove that for all $n\geq 2$ and $k\geq 5$ the following inequalities hold: $({k-3}/2)^{n/2}(\frac{k-1}2)^{n/2} < log_2 Q(n,k) \leq {c_k(k-2)^{n}}
Krotov, Denis, Potapov, Vladimir
core   +2 more sources

Pentagonal quasigroups, their translatability and parastrophes

Open Mathematics, 2021
Any pentagonal quasigroup QQ is proved to have the product xy=φ(x)+y−φ(y)xy=\varphi \left(x)+y-\varphi (y), where (Q,+)\left(Q,+) is an Abelian group, φ\varphi is its regular automorphism satisfying φ4−φ3+φ2−φ+ε=0{\varphi }^{4}-{\varphi }^{3}+{\varphi }^
Dudek Wieslaw A., Monzo Robert A. R.
doaj   +1 more source