Introduction to Quadratic Forms over Fields

Lam, T. Y. (2005). Introduction to Quadratic Forms over Fields.

Type

Book

Intellectual base

Textbook

Year

2005

ISBN

9780821831091

Link

no authoritative link yet

Cited by

5 citations across 5 artifacts.

Domain-specific

• Euclidean ordered field
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Hurwitz problem
  • … and output dimensions, quadratic forms, bilinear coordinate functions, exact composition identity, admissible coefficient class, existence bounds and relation to division algebras are explicit. to An applied instance preserves the invariant under changed notation, scale, dataset, jurisdiction, or implementation..
• Ordered field
  • … and operations, total order or positive cone, trichotomy, translation invariance, positive-product closure, characteristic consequences and any Archimedean or completeness assumptions are explicit. to An applied instance preserves the invariant under changed notation, scale, dataset, jurisdiction, or implementation..
• Quadratic Space
  • Over finite fields and number fields, isotropy, discriminants, local invariants, and Witt decomposition take the leading roles; Lam provides the specialist field-based treatment behind this scope.
• Universal quadratic form
  • Universality depends on the base ring, integrality, positivity and allowed vectors; over integers, forms representing all positive integers connect to local-global criteria and finite test theorems.

Verification

This reference passed the adversarial substantiation pipeline: it was checked to exist and to support the claim it is attached to. See how references were verified.

Registry ID ref:3e1ffe7cc502 · see in the full table