Amitsur--Small Extensions and a Skew Amitsur--Small Theorem

TL;DR

This paper generalizes the Amitsur--Small Theorem to a skew setting by introducing Amitsur--Small extensions, expanding the theorem's applicability in algebraic structures.

Contribution

It introduces Amitsur--Small extensions and proves a skew version of the Amitsur--Small Theorem, extending existing algebraic results.

Findings

Established a new framework for skew algebraic structures.

Proved a generalized version of the Amitsur--Small Theorem.

Enhanced understanding of algebraic extensions in skew contexts.

Abstract

We introduce the notion of Amitsur--Small extensions to generalize a key lemma underlying the Amitsur--Small Theorem to the skew setting. Building on this framework, we establish a skew version of the Amitsur--Small Theorem.