Hilbert's basis theorem for non-associative and hom-associative Ore extensions

TL;DR

This paper extends Hilbert's basis theorem to hom-associative and non-associative Ore extensions, developing hom-module theory and demonstrating that these extensions are noetherian under the new framework.

Contribution

It introduces a hom-associative version of Hilbert's basis theorem, unifying non-associative and classical cases, and develops related hom-module theory.

Findings

Hom-associative Ore extensions are noetherian under the new theorem.

The paper develops foundational hom-module theory.

Examples demonstrate the applicability to non-associative and hom-associative structures.

Abstract

We prove a hom-associative version of Hilbert's basis theorem, which includes as special cases both a non-associative version and the classical associative Hilbert's basis theorem for Ore extensions. Along the way, we develop hom-module theory. We conclude with some examples of both non-associative and hom-associative Ore extensions which are all noetherian by our theorem.