Results 21 to 30 of about 1,397 (124)

Some Algebraic Properties of the Wilson Loop

Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022
In this article, some algebraic properties of the Wilson loop have been investigated in a broad manner. These properties include identities, autotopisms, and implications. We use some equivalent conditions to study the behavior of holomorphism of this loop. Under the shadow of this holomorphism, we are able to observe coincident loops.
Han Li, M. Nadeem, M. A. Ali, H. Mutee ur Rehman, Yuan Yi   +4 more
wiley   +1 more source

Classification of quasigroups according to directions of translations I [PDF]

, 2020
summary:It is proved that every translation in a quasigroup has two independent parameters. One of them is a bijection of the carrier set. The second parameter is called a direction here.
Lutsenko, Alla, Sokhatsky, Fedir
core   +1 more source

[Retracted] Double Weak Hopf Quiver and Its Path Coalgebra

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
The main input of this research is the introduction of the concept of double weak Hopf quiver (DWHQ). In addition, the structures of weak Hopf algebra (WHA) are obtained through path coalgebra of the proposed quivers. Furthermore, the module and comodule structures on the said WHA are discussed.
Muhammad Naseer Khan, Munir Ahmed, Muhammad Arshad, Waleed Almutiry, Rashad A. R. Bantan, Mohammed Elgarhy, Muhammad Gulzar   +6 more
wiley   +1 more source

A Pair of Smarandachely Isotopic Quasigroups and Loops of the Same Variety [PDF]

, 2008
The isotopic invariance or universality of types and varieties of quasigroups and loops described by one or more equivalent identities has been of interest to researchers in loop theory in the recent past.
Gbolahan, Temitope
core   +1 more source

$F$-quasigroups isotopic to Moufang loops [PDF]

, 1979
summary:In Kepka T., Kinyon M.K., Phillips J.D., {\it The structure of F-quasigroups\/}, {\tt math.GR/0510298}, we showed that every loop isotopic to an F-quasigroup is a Moufang loop.
Kinyon, Michael K., Phillips, J. D., Kepka, Tomáš   +2 more
core   +1 more source

An holomorphic study of Smarandache automorphic and cross inverse property loops [PDF]

, 2008
By studying the holomorphic structure of automorphic inverse property uasigroups and loops[AIPQ and (AIPL)] and cross inverse property quasigroups and loops[CIPQ and (CIPL)], it is established that the holomorph of a loop is a Smarandache; AIPL, CIPL, K ...
Gbolahan, Temitoe, Temitope Gbolahan Jaiyeola   +1 more
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

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

Ternary quasigroups and the modular group [PDF]

, 2006
summary:For a positive integer $n$, the usual definitions of $n$-quasigroups are rather complicated: either by combinatorial conditions that effectively amount to Latin $n$-cubes, or by $2n$ identities on $n+1$ different $n$-ary operations. In this paper,
Smith, Jonathan D. H., Smith, Jonathan
core   +3 more sources

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