Sobre polin?omios centrais em uma e duas vari′aveis para M2(K) quando K ′e um corpo finito On central polynomials in one and two variables for M2(K) when K is a finite field

摘要

Let K be a finite field with q elements and let M2(K) be the matrix algebra of ordertwo over K. We know some examples of central polynomials but the basis of centralpolynomials of M2(K) is unknown. In this paper we exhibit a central polynomialc(x) in one variable for M2(K) such that every central polynomial in one variable isa multiple of c(x).We also exhibit a conjecture for the basis of the central polynomials for M2(K).