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Representation of a Full Transformation Semi-group Over a Finite Field

Abstract

In this paper we discuss the representations of a full transformation semigroup over a finite field. Furthermore, we observe some properties of irreducibility representation of a full transformation semigroup and discuss the linear representation of a zero-adjoined full transformation semigroup. Moreover, we characterize the linear representation of a full transformation semigroup over a finite field Fq (where q is a prime power) in terms of Maschke’s Theorem. Finally, we observe that there exists an isomorphism between the full matrix algebra (Fq)m and the space of all linear transformation L(Fq m) on an m-dimensional vector space Fq m

Munir Ahmed, Muhammad Naseer Khan, Muhammad Afzal Rana

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