A generalisation of Amitsur's A-polynomials

TL;DR

This paper explores polynomials in a skew polynomial ring whose eigenrings form central simple algebras over a specific field, expanding understanding of their algebraic structure.

Contribution

It provides new examples of polynomials with eigenrings that are central simple algebras, generalizing Amitsur's A-polynomials.

Findings

Eigenrings of certain skew polynomials are central simple algebras.

Identification of conditions under which eigenrings are central simple.

Extension of Amitsur's A-polynomials to broader classes.

Abstract

We find examples of polynomials $f\in D[t;\sigma,\delta]$ whose eigenring $\mathcal{E}(f)$ is a central simple algebra over the field $F = C \cap {\rm Fix}(\sigma) \cap {\rm Const}(\delta)$.