Séminaires : Séminaire Général de Logique

Equipe(s) : lm,
Responsables :O. Finkel, T. Ibarlucía, A. Khélif, S. Rideau, C. Sureson
Email des responsables :
Salle : salle 2015
Adresse :Sophie Germain
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Orateur(s) L'exposé de Francisco Miraglia prévu le 30 janvier est annulé - Université de Sao Paulo, Brésil,
Titre Abstract Algebraic Theory of Quadratic Forms and Rings
Date30/01/2017
Horaire15:10 à 16:10
Résume
Abstract (joint work with M. Dickmann):

Let A be a commutative unitary semi-real (– 1 is not a sum of squares) ring in which 2 is a unit; let T = A2 or a proper preorder of A. We shall describe first order axioms such that if the pair (A, T) is a model of these statements, then there is a special group, $G_T(A)$, naturally associated to (A, T), faithfully coding the T-theory of diagonal quadratic forms with unit coefficients in A. Under mild restrictions, these axioms are necessary and sufficient for $G_T(A)$ to faithfully code representation and T-isometry of non-singular diagonal quadratic forms with coefficients in A.

We shall present important classes of rings satisfying these axioms and extract significant results concerning the behavior of quadratic form theory over these classes of rings. The needed concepts will be presented during the talk, which contains only part of the results that appeared in:

M. Dickmann, F. Miraglia, Faithfully Quadratic Rings, Memoirs of the AMS, 1128, (November 2015).
Sallesalle 2015
AdresseSophie Germain
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