Standard polynomials are characterized by their degree and exponent

By the Giambruno–Zaicev theorem (Giambruno and Zaicev, 1999) [5], , the exponent exp(A) of a p.i. algebra A exists, and is always an integer. In Berele and Regev (2001) [2] it was shown that the exponent exp(Stn) of the standard polynomial Stn of degree n is not smaller than the exponent of any polynomial of degree n. Here it is proved that exp(Stn) is strictly larger than the exponent of any other polynomial of degree n which is not a multiple of Stn.