Witt rings of quadratically presentable fields | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 2، دوره 12، شماره 1، فروردین 2020، صفحه 1-23 اصل مقاله (652.12 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.29252/cgasa.12.1.1 | ||
| نویسندگان | ||
| Pawel Gladki1؛ Krzysztof Worytkiewicz2 | ||
| 1Institute of Mathematics, Faculty of Mathematics, Physics and Chemistry, University of Silesia | ||
| 2Laboratorire de Math'{e}matiques, Universit'{e} Savoie Mont Blanc, B^{a}timent Le Chablais, Campus Scientifique, 73376 Le Bourget du Lac, France. | ||
| چکیده | ||
| This paper introduces an approach to the axiomatic theory of quadratic forms based on $presentable$ partially ordered sets, that is partially ordered sets subject to additional conditions which amount to a strong form of local presentability. It turns out that the classical notion of the Witt ring of symmetric bilinear forms over a field makes sense in the context of $quadratically\ presentable\ fields$, that is, fields equipped with a presentable partial order inequationaly compatible with the algebraic operations. In particular, Witt rings of symmetric bilinear forms over fields of arbitrary characteristics are isomorphic to Witt rings of suitably built quadratically presentable fields. | ||
| کلیدواژهها | ||
| Quadratically presentable fields؛ Witt rings؛ hyperfields؛ quadratic forms | ||
| مراجع | ||
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