{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/normal-quaternionic-matrices-and-finitely","title":"Normal Quaternionic Matrices and Finitely Generated Witt Rings","arxiv_id":"2505.14485","date":"2025-05-20","proceeding":null,"authors":["Nico Lorenz","Alexander Schönert"],"abstract":"We present a new approach to verify the Elementary Type Conjecture for abstract Witt rings with small number of square classes. To do so, we make use of an abstract analogue of the 2-torsion part of the Brauer group. We develop a description of the entire structure of an abstract Witt ring with $2^n$ square classes in terms of a unique $n\\times n$ matrix satisfying a small additional condition that particularly holds for Witt rings of fields. Via computational search, we find all these matrices for $n$ up to $7$. This verifies that all Witt rings of fields with up to $128$ square classes are of elementary type.","url_abs":"https://arxiv.org/abs/2505.14485v1","url_pdf":"https://arxiv.org/pdf/2505.14485v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"normal-quaternionic-matrices-and-finitely","repo_url":"https://github.com/nicolo314/normalquaternionicmatrices","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}