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 -