M. J. Ibrahim

On Presentations of Semigroup of Transformations Restricted by an Equivalence

M. J. Ibrahim & D. A. Oluyori · Asian Research Journal of Mathematics · 2023

For a non-empty set X denote the full transformation semigroup of X by T(X). Let \(\sigma\) be an equivalence relation on X and E(X, \(\sigma\)) denotes the semigroup (under composition) of all \(\alpha\) : X \(\mapsto\) X, such that \(\sigma\) \(\subseteq\) ker(\(\alpha\) ). Sem...

Open access Research Article 10.9734/arjom/2023/v19i2643

Rank of the Subsemigroup of the Semigroup of Finite Full Contraction Maps Generated by Elements of Defect One

A. T. Imam, M. Balarabe & M. J. Ibrahim · Journal of Advances in Mathematics and Computer Science · 2019

Let Tn be the semigroup of full transformation on a nite set n. Then, a map ∈ Tn is said to be a contraction, if for all x; y ∈ Xn, |x − y| ≤ |x − y|. Let CTn denote the subsemigroup of all contraction maps in Tn. In this paper we calculated the rank of the subsemigroup of CTn ge...

Open access Research Article 10.9734/JAMCS/2019/41513