Education

• 1993

  Bachelor degree from MathematicsCollege of Sience, King Abdulaziz University in Jeddah, جدة, المملكة العربية السعودية

• 2001

  Master degree from MathematicsSchool of Mathematical and Physical Sciences, University of Sussex at Brighton, Brighton, بريطانيا

• 2009

  Doctorate degree from MathenaticsSchool of Mathematics, University of Southampton, , بريطانيا

Employment

Research Interests

I am intersting in semigroup theory. In particular, I have a good knowledg about the concept of inverse transversals of a cerian type of semigroup known as regular semigroups. This concept arises in response to natural questions concerning the greatest idempotent in a naturally orderd regular semigroup. Much of the efforts has focused on two aspects of the theory: (i) the structure of those regular semigroups which contain transversals and (ii) a natural classification scheme for different type

A semigroup is a set with an associative multiplication defined on it. Unlike groups, in semigroups the identity may or may not exist. Moreover, the elements of a semigroup may not have inverse and may have more than one inverse. A regular semigroup is a semigroup for which each element has an (at least one) inverse. An inverse semigroup is a semigroup for which each element has a unique inverse.

If S is a regular semigroup, then by an inverse transversal of S we mean an inverse subsemigroup T of S that contains exactly one inverse of each element of S. This concept was introduced in 1978 by T. S. Blyth and a lot of work on the structure of such semigroups has been done. Much of the efforts have been focused on two aspects of the theory: the structure of those regular semigroups which contain transversals, and a natural classification scheme for different types of transversals.

The generalisation of these concepts is a quite interesting area of research. There are different paths of generalising regular semigroups that admit inverse transversals. One that is of my interests is the abundant semigroups with adequate transversals. In that area, the very challenging question of structure theorems for adequate transversals have been tackled and still lots of open problems.

In addition to Semigroup Theory, I am also interested in Ring Theory and Graph Theory.

s of transversals. The generalization of these concepts is quite interesting area of research. There are different pathes of generalizing  regualr semigroups that admit inverse transversals. One of them, that was of my interest, is abundant semigroups with adequate transversals. In that area, the very challenging question of structure theorems for adequate transversals have been tackled and still lots of open problems. 

In addition to semigroup theorey, I have some interest in Ring theory. 

Scientific interests

Courses

Areas of expertise