6533b835fe1ef96bd129f747

RESEARCH PRODUCT

Standard polynomials are characterized by their degree and exponent

Amitai RegevAntonio Giambruno

subject

Discrete mathematicsPolynomialAlgebra and Number TheoryQuantitative Biology::Neurons and CognitionDegree (graph theory)ExponentPolynomial identityCodimensionsCombinatoricsIntegerExponentDegree of a polynomialAlgebra over a fieldPolynomial identity Exponent CodimensionsMathematics

description

Abstract 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 ( St n ) of the standard polynomial St n of degree n is not smaller than the exponent of any polynomial of degree n. Here it is proved that exp ( St n ) is strictly larger than the exponent of any other polynomial of degree n which is not a multiple of St n .

yearjournalcountryeditionlanguage
2011-06-01
10.1016/j.jalgebra.2011.03.030http://hdl.handle.net/10447/60568