ON SUBALGEBRAS OF n× n MATRICES NOT SATISFYING IDENTITIES OF DEGREE 2n− 2
نویسنده
چکیده
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 ≤ 2n − 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.
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