Non-associative versions of Hilbert's basis theorem

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.

9 pages. Earlier versions of arXiv:2207.07994 have been split in two; this is the second part; corrected some typos; minor update