Cayley Hamilton theorem with sandwich coefficients for n$\times$n matrices over a ring satisfying [x,y][u,v]=0

Abstract

If A is an n \times n matrix over a ring R satisfying the polynomial identity [x,y][u,v]=0, then an invariant Cayley-Hamilton identity of the form ΣA^{i}c_{i,j}A^{j}=0 with c_{i,j}\in R and c_{n,n}=(n!)^2 holds for A.