
TL;DR
This paper investigates the growth behavior of central polynomials in specific algebraic structures, revealing that matrix algebras satisfy numerous proper central polynomials, which enhances understanding of their polynomial identities.
Contribution
It provides new insights into the growth rates of central polynomials for the Grassmann algebra and matrix algebras, highlighting their abundance of proper central polynomials.
Findings
Matrix algebras satisfy many proper central polynomials
Growth rates of central polynomials are characterized for specific algebras
Enhanced understanding of polynomial identities in algebraic structures
Abstract
We study the growth of the central polynomials for the algebras and , the infinite dimensional Grassmann algebra and the matrices over a field of characteristic zero. In particular it follows that satisfy many proper central polynomials.
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