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We introduce non-associative skew Laurent polynomial rings over unital,non-associative rings. We prove simplicity results and a Hilbert's basistheorem for these. We also prove several versions of Hilbert's basis theoremfor non-associative Ore extensions and non-associative generalizations of skewpower series rings and skew Laurent series rings. For non-associative skewLaurent polynomial rings, we show that both a left and a right version ofHilbert's basis theorem hold. For non-associative Ore extensions, we show thata right version holds, but give a counterexample to a left version; adifference that does not appear in the associative setting.

Hilbert's basis theorem and simplicity for non-associative skew Laurent polynomial rings and related rings