Abstract
We prove a hom-associative version of Hilbert’s basis theorem, which includes as special cases both a non-associative version and the classical Hilbert’s basis theorem for associative Ore extensions. Along the way, we develop hom-module theory. We conclude with some examples of both non-associative and hom-associative Ore extensions which are all noetherian by our theorem.
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Acknowledgements
We wish to thank Patrik Lundström for pointing out that the associator identity could be used in proving Proposition 7 in a simpler way than was originally done. We would also like to thank Lars Hellström for providing the unital hom-ring in Example 7, and the referee for giving concrete suggestions on how to improve the article.
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Open access funding provided by Mälardalen University.
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Presented by: Kenneth Goodearl
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Bäck, P., Richter, J. Hilbert’s Basis Theorem for Non-associative and Hom-associative Ore Extensions. Algebr Represent Theor 26, 1051–1065 (2023). https://doi.org/10.1007/s10468-022-10123-8
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DOI: https://doi.org/10.1007/s10468-022-10123-8
Keywords
- Hilbert’s basis theorem
- Hom-associative algebras
- Hom-associative Ore extensions
- Hom-modules
- Non-commutative noetherian rings