Non-associative versions of Hilbert's basis theorem
Rings and Algebras
2025-03-21 v3
Abstract
We prove several new versions of Hilbert's basis theorem for non-associative Ore extensions, non-associative skew Laurent polynomial rings, non-associative skew power series rings, and non-associative skew Laurent series rings. For non-associative skew Laurent polynomial rings, we show that both a left and a right version of Hilbert's basis theorem hold. For non-associative Ore extensions, we show that a right version holds, but give a counterexample to a left version; a difference that does not appear in the associative setting.
Keywords
Cite
@article{arxiv.2404.16889,
title = {Non-associative versions of Hilbert's basis theorem},
author = {Per Bäck and Johan Richter},
journal= {arXiv preprint arXiv:2404.16889},
year = {2025}
}
Comments
9 pages. Earlier versions of arXiv:2207.07994 have been split in two; this is the second part; corrected some typos; minor update