Centralizers in Free Associative Algebras and Generic Matrices

TL;DR

This paper completes the proof of the Bergman centralizer theorem using generic matrices and shows that the algebra of generic matrices with characteristic coefficients is integrally closed.

Contribution

It finalizes the Bergman centralizer theorem proof with a new approach and proves the integrally closed property of the algebra of generic matrices.

Findings

Complete proof of the Bergman centralizer theorem.

Algebra of generic matrices with characteristic coefficients is integrally closed.

Abstract

This paper is concerned with the completion of the proof of the Bergman centralizer theorem by using generic matrices based on our previous quantization proof \cite{KBRZh}. Additionally, we establish that the algebra of generic matrices with characteristic coefficients is integrally closed.