Skew fields not finitely generated as algebras

[2604.18480] Skew fields not finitely generated as algebras Skip to main content Search Submit Donate Log in Mathematics > Rings and Algebras arXiv:2604.18480 (math) [Submitted on 20 Apr 2026 ( v1 ), last revised 26 Aug 2026 (this version, v2)] Title: Skew fields not finitely generated as algebras Authors: K. R. Goodearl , E. S. Letzter View PDF HTML (experimental) Abstract: An associative division algebra D is said to be _affine_ over a central subfield k if D is finitely generated as a k-algebra. In 1956 Amitsur famously proved that, when k is uncountable, D cannot be k-affine unless D is algebraic over k. In this paper we consider affineness -- and nonaffineness -- for certain naturally occurring classes of division algebras over arbitrary fields. The primary applications are to division algebras of fractions of suitably conditioned iterated skew polynomial rings over k, including many examples naturally arising in Lie theoretic and quantum group settings. Many transcendental division algebras are thus verified to be nonaffine over k. Division algebras of fractions of Weyl algebras and quantum affine spaces are determined to be affine over their centers exactly when they are finite dimensional over their centers. Comments: Revised. To appear in Contemporary Mathematics, combined proceedings for the workshops "Revisiting Fundamental Problems: Infinite Dimensional Division Algebras -- Algebraicity and Finiteness" and the "Seattle Noncommutative Algebra Conference." Title has been shortened, per referee's recommendation, from the original, "`New' examples of skew fields not finitely generated as algebras." Subjects: Rings and Algebras (math.RA) MSC classes: Primary: 16K40, 16S15. Secondary: 16E60, 16P40 Cite as: arXiv:2604.18480 [math.RA] (or arXiv:2604.18480v2 [math.RA] for this version) https://doi.org/10.48550/arXiv.2604.18480 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Edward S. Letzter [ view email ] [v1] Mon, 20 Apr 2026 16:34:47 UTC (12 KB) [v2] Wed, 26 Aug 2026 20:04:28 UTC (13 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.RA < prev | next > new | recent | 2026-04 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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