TY - JOUR ID - 87412 TI - Witt rings of quadratically presentable fields JO - Categories and General Algebraic Structures with Applications JA - CGASA LA - en SN - 2345-5853 AU - Gladki, Pawel AU - Worytkiewicz, Krzysztof AD - Institute of Mathematics, Faculty of Mathematics, Physics and Chemistry, University of Silesia AD - Laboratorire de Math'{e}matiques, Universit'{e} Savoie Mont Blanc, B^{a}timent Le Chablais, Campus Scientifique, 73376 Le Bourget du Lac, France. Y1 - 2020 PY - 2020 VL - 12 IS - 1 SP - 1 EP - 23 KW - Quadratically presentable fields KW - Witt rings KW - hyperfields KW - quadratic forms DO - 10.29252/cgasa.12.1.1 N2 - 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. UR - https://cgasa.sbu.ac.ir/article_87412.html L1 - https://cgasa.sbu.ac.ir/article_87412_e4ca569b071e83128b5db22ac6d06101.pdf ER -