Verification of a Conjecture of Gerstenhaber

J. P. Jans
1960 Proceedings of the American Mathematical Society  
Let Tn denote the algebra of matrices (An) where -4<, = 0 for *áj and AijÇzF, a field. In a recent paper [l], M. Gerstenhaber conjectured that Tn/Tl could not be represented by «X« matrices if w^5 and 3^k^n -1. He proved there that the conjecture is true for k = n-l. The purpose of this note is to verify this conjecture in general. In fact, we shall prove something a bit stronger.
doi:10.2307/2034772 fatcat:rovep25g4fgrzaf34tqjnnfekm