A Cayley-Hamilton trace identity for 2 × 2 matrices over Lie-solvable rings
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First we construct an algebra satisfying the polynomial identity [[x,y],[u,v]]=0, but none of the stronger identities [x,y][u,v]=0 and [[x,y],z]=0. Then we exhibit a Cayley-Hamilton trace identity for 2×2 matrices with entries in a ring R satisfying [[x,y],[x,z]]=0 and 12∈R. © 2011 Elsevier Inc. All rights reserved.