Quadratic forms over fields

K. Szymiczek

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1977

Abstract

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CONTENTSIntroduction.................................................................................................................................. 5Chapter I. Preliminaries oil round and Pfister forms.......................................................... 8Chapter II. Basic properties of the Grothendieck ring......................................................... 11 § 1. Prime ideals in G(F)...................................................................................................... 11 § 2. Elements of special types............................................................................................ 15 § 3. Local properties of G(F)................................................................................................ 20Chapter III. Group structure of G(F) and W(F)....................................................................... 23 §1. General decomposition theorems.............................................................................. 23 § 2. Value sets of binary forms and the group structure of G(F) and W(F)................. 28 § 3. The rank of G(F) and W(F)............................................................................................ 32Chapter IV. Equivalence of fields with respect to quadratic forms.................................... 36 § 1. G-equivalences.............................................................................................................. 36 § 2. W-equivalences.............................................................................................................. 41 § 3. Comparisons.................................................................................................................. 43Chapter V. A Galois correspondence in the quadratic form theory.................................. 46 § 1. The binary case............................................................................................................. 46 § 2. A generalization.............................................................................................................. 54Chapter VI. Field constructions................................................................................................ 57Chapter VII. Open problems..................................................................................................... 60References.................................................................................................................................. 62

How to cite

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K. Szymiczek. Quadratic forms over fields. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1977. <http://eudml.org/doc/268520>.

@book{K1977,
abstract = {CONTENTSIntroduction.................................................................................................................................. 5Chapter I. Preliminaries oil round and Pfister forms.......................................................... 8Chapter II. Basic properties of the Grothendieck ring......................................................... 11 § 1. Prime ideals in G(F)...................................................................................................... 11 § 2. Elements of special types............................................................................................ 15 § 3. Local properties of G(F)................................................................................................ 20Chapter III. Group structure of G(F) and W(F)....................................................................... 23 §1. General decomposition theorems.............................................................................. 23 § 2. Value sets of binary forms and the group structure of G(F) and W(F)................. 28 § 3. The rank of G(F) and W(F)............................................................................................ 32Chapter IV. Equivalence of fields with respect to quadratic forms.................................... 36 § 1. G-equivalences.............................................................................................................. 36 § 2. W-equivalences.............................................................................................................. 41 § 3. Comparisons.................................................................................................................. 43Chapter V. A Galois correspondence in the quadratic form theory.................................. 46 § 1. The binary case............................................................................................................. 46 § 2. A generalization.............................................................................................................. 54Chapter VI. Field constructions................................................................................................ 57Chapter VII. Open problems..................................................................................................... 60References.................................................................................................................................. 62},
author = {K. Szymiczek},
keywords = {Grothendieck ring; Witt ring; fields of characteristic not 2},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Quadratic forms over fields},
url = {http://eudml.org/doc/268520},
year = {1977},
}

TY - BOOK
AU - K. Szymiczek
TI - Quadratic forms over fields
PY - 1977
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTSIntroduction.................................................................................................................................. 5Chapter I. Preliminaries oil round and Pfister forms.......................................................... 8Chapter II. Basic properties of the Grothendieck ring......................................................... 11 § 1. Prime ideals in G(F)...................................................................................................... 11 § 2. Elements of special types............................................................................................ 15 § 3. Local properties of G(F)................................................................................................ 20Chapter III. Group structure of G(F) and W(F)....................................................................... 23 §1. General decomposition theorems.............................................................................. 23 § 2. Value sets of binary forms and the group structure of G(F) and W(F)................. 28 § 3. The rank of G(F) and W(F)............................................................................................ 32Chapter IV. Equivalence of fields with respect to quadratic forms.................................... 36 § 1. G-equivalences.............................................................................................................. 36 § 2. W-equivalences.............................................................................................................. 41 § 3. Comparisons.................................................................................................................. 43Chapter V. A Galois correspondence in the quadratic form theory.................................. 46 § 1. The binary case............................................................................................................. 46 § 2. A generalization.............................................................................................................. 54Chapter VI. Field constructions................................................................................................ 57Chapter VII. Open problems..................................................................................................... 60References.................................................................................................................................. 62
LA - eng
KW - Grothendieck ring; Witt ring; fields of characteristic not 2
UR - http://eudml.org/doc/268520
ER -

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