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

Research & Reviews: Journal of Statistics and Mathematical Sciences

article

Munir Ahmed¹  Muhammad Naseer Khan²  Muhammad Afzal Rana² 

[1] Department of Mathematics, Islamabad Model College For Boys;Department Of Mathematics and Statistics, Riphah International University

关键词: Semigroup of transformations;    Representation of semigroup;    Finite field;   

来源: Research & Reviews

【 摘 要 】

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.

【 授权许可】

Unknown