In 1903, Hilbert [4] introduced a ring of formal Laurent series with a skewed or twisted multiplication to show the existence of a non-commutative ordered division ring. Nowadays, the rings and their corresponding multiplication are thus referred to as skew or twisted Laurent series rings and Hilbert’s twist [6], respectively. Thirty years later, Ore [12] initiated the study of what he called ‘non-commutative polynomial rings’, today more commonly known as Ore extensions. Since their introductions, skew Laurent series rings, Ore extensions and the closely related skew Laurent polynomial rings have been studied quite extensively (see e.g. [3, 6, 7] for comprehensive introductions). Moreover, some years ago, Nystedt, Öinert and Richter [10] introduced a non-associative generalization of Ore extensions.

We introduce non-associative skew Laurent polynomial rings and characterize when they are simple. Thereby, we generalize results by Jordan, Voskoglou, and Nystedt and Öinert.