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

Abstract: We introduce non-associative skew Laurent polynomial rings over unital, non-associative rings. We prove simplicity results and a Hilbert's basis theorem for these. We also prove several versions of Hilbert's basis theorem for non-associative Ore extensions and non-associative generalizations of skew power series rings and 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.