Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585312120200101Witt rings of quadratically presentable fields1238741210.29252/cgasa.12.1.1ENPawel GladkiInstitute of Mathematics, Faculty of Mathematics, Physics and Chemistry, University of SilesiaKrzysztof WorytkiewiczLaboratorire de Math'{e}matiques, Universit'{e} Savoie Mont Blanc, B^{a}timent Le Chablais, Campus Scientifique, 73376 Le Bourget du Lac, France.Journal Article20180426This 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.https://cgasa.sbu.ac.ir/article_87412_e4ca569b071e83128b5db22ac6d06101.pdf