Meet ABDULKAREEM OLALEKAN ABDULAFEEZ, an Academic Staff of Lagos State University.
Algebra
Lecturer II
Mathematics
At the Mathematics department office
Appointment on Visitation important
Topic: Group Theory And Its Generalisation
Description: This research concerns studies on quasigroups and loops theory. I have conducted research in Bol loops, Moufang loops, generalised Bol loops, Middle Bol loops, Cheban loops, etc which have led to publications of several articles in reputable peer-review journals.
| # | Certificate | School | Year |
|---|---|---|---|
| 1. | Ph.D (Mathematics/Non Associative Algebra and Loop Theory) | Federal University of Agriculture Abeokuta | 2021 |
A Study of biquasigroup satisfying some Stein Identity
If $(Q,circ)$ and $(Q,ast)$ are quasigroups which satisfy $(acirc b) ast (b circ c)=a ast b$, then $(Q, circ, ast)$ is said to be ward double quasigroup. Polonijo prove that for any ward double quasigroup $(Q, circ, ast)$, there is a group $(Q, cdot)$ and bijections $alpha$ and $eta$ on Q such that $xcirc y=x-eta y$, $xast y=alpha(x-y)$. Starting from any group $(G,circ )$ we can form a Ward quasigroup $(G,ast)$ by defining $xast y=x circ y^{-1}$ that is, $ast$ is the operation of right division in the group $(G,circ )$.
Biquasigroups have a richer structural property than quasigroups since it consists of two independent quasigroup operations. This enables it to have more intricate definitions and can model more complex systems than a quasigroup. This work determines the structure of biquasigroups $(Q,circ, ast)$ satisfying variations of the Stein's third and second identities; $(xcirc y)ast (y circ x)=y$, $xycirc x = ycirc xy$. It is an attempt to find out whether there are biquasigroups that obey the Stein's third second identities and obtain the different forms in which such biquasigroups exist in relation to the binary operations involved. The study obtained conditions for which a biquasigroup obey the Stein's third and second identities and the conditions are used to generate several examples of biquasigroups that obey the Stein's third and second identities.
ABDULKAREEM ABDULAFEEZ is a Lecturer II at the Department of Mathematics
ABDULKAREEM has a Ph.D in Mathematics/Non Associative Algebra and Loop Theory from Federal University of Agriculture Abeokuta
