Non-associative versions of Hilbert’s basis theorem
Volume 176 / 2024
Colloquium Mathematicum 176 (2024), 135-145
MSC: Primary 17A99; Secondary 17D99, 16S35, 16S36, 16W50, 16W70
DOI: 10.4064/cm9419-9-2024
Published online: 21 October 2024
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.
