Faithfully quadratic rings

Faithfully quadratic rings / M. Dickmann, F. Miraglia.

In this monograph we extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where -1 is not a sum of squares and 2 is invertible. We accomplish this by: (1) Extending the classical noti...

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Bibliographic Details
Main Authors: Dickmann, M. A., 1940- (Author), Miraglia, Francisco (Author)
Format: eBook
Language:English
Published: Providence, Rhode Island : American Mathematical Society, 2015.
Series:Memoirs of the American Mathematical Society ; no. 1128.
Subjects:
Forms, Quadratic.
Commutative rings.
Commutative rings
Forms, Quadratic
Quadratische Form
Kommutativer Ring
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Table of Contents:
  • Preface
  • Basic concepts
  • Rings and special groups
  • The notion of T-faithfully quadratic ring. Some basic consequences
  • Idempotents, products and T-isometry
  • First-order axioms for quadratic faithfulness
  • Rings with many units
  • Transversality of representation in p-rings with bounded inversion
  • Reduced f-rings
  • Strictly representable rings
  • Quadratic form theory over faithfully quadratic rings
  • Bibliography
  • Index of symbols
  • Subject index.

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