The unit group of algebra of circulant matrices

Abstract

Let $Cr_{n}(F)$ denote the algebra of $ntimes n$ circulant matrices over the field $F$‎. ‎In this paper‎, ‎we study the unit group of $Cr_{n}(mathbb{F}_{p^{m}})$‎, ‎where $mathbb{F}_{p^{m}}$ denotes the Galois field of order $p^{m},~p$ prime‎.