Faithfully Quadratic Rings

M. Dickmann, F. Miraglia (Autoren)

Buch | Softcover

129 Seiten

2015
American Mathematical Society (Verlag)
978-1-4704-1468-9 (ISBN)

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In this monograph the authors 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. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of $T$-isometry, where $T$ is a preorder of the given ring, $A$, or $T = A^2$. (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in the field case.

M. Dickmann, Institut de Mathematiques de Jussieu-Paris Rive Gauche, France. F. Miraglia, University of Sao Paulo, Brasil.

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

Erscheinungsdatum	09.12.2015
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	280 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
ISBN-10	1-4704-1468-6 / 1470414686
ISBN-13	978-1-4704-1468-9 / 9781470414689
Zustand	Neuware