Witt rings of quadratically presentable fields

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Gladki Pawel; Worytkiewicz Krzysztof

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Journal: CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS Year:2020 | Volume:12 | Issue:1 Page(s): 1-23

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Information Journal Paper

Title

Witt rings of quadratically presentable fields

Author(s)

Gladki Pawel | Worytkiewicz Krzysztof | Issue Writer Certificate

Keywords

Quadratically presentable fieldsQ4

Witt ringsQ4

hyperfieldsQ4

quadratic formsQ4

Abstract

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.

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APA: Copy

Gladki, Pawel, & Worytkiewicz, Krzysztof. (2020). Witt rings of quadratically presentable fields. CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS, 12(1 ), 1-23. SID. https://sid.ir/paper/255392/en

Vancouver: Copy

Gladki Pawel, Worytkiewicz Krzysztof. Witt rings of quadratically presentable fields. CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS[Internet]. 2020;12(1 ):1-23. Available from: https://sid.ir/paper/255392/en

IEEE: Copy

Pawel Gladki, and Krzysztof Worytkiewicz, “Witt rings of quadratically presentable fields,” CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS, vol. 12, no. 1 , pp. 1–23, 2020, [Online]. Available: https://sid.ir/paper/255392/en

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