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arXiv · 2404.16889

Non-associative versions of Hilbert's basis theorem

Per Bäck·Johan Richter
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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.

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Per Bäck, Johan Richter. 2024-04-24. Non-associative versions of Hilbert's basis theorem. https://doi.org/10.4064/cm9419-9-2024

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