On subalgebras of n×n matrices not satisfying identities of degree 2n−2 Original Research Article

The Amitsur–Levitzki theorem asserts that Mn(F) satisfies a polynomial identity of degree 2n. (Here, F is a field and Mn(F) is the algebra of n×n matrices over F.) It is easy to give examples of subalgebras of Mn(F) that do satisfy an identity of lower degree and subalgebras of Mn(F) that satisfy no polynomial identity of degree less-than-or-equals, slant2n−2. In this paper we prove that the subalgebras of n×n matrices satisfying no nonzero polynomial of degree less than 2n are, up to F-algebra isomorphisms, the class of full block upper triangular matrix algebras.