Séminaires : Structures algébriques ordonnées

Equipe(s) : lm,
Responsables :F. Delon, M. Dickmann, D. Gondard
Email des responsables : dickmann@math.univ-paris-diderot.fr
Salle : 1013
Adresse :Sophie Germain

Mardi de 14h00 à 15h45
Page du séminaire et programme
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Orateur(s) Hugo Mariano - Université de Sao Paulo, Brésil,
Titre Multirings and applications to algebraic theory of quadratic forms, III
Horaire14:00 à 15:45
(Joint work with Hugo R.O. Ribeiro (IME-USP))
In this third talk, we focus on constructions of multirings associated with real semigroups:
(i) we describe further properties of the functor Q, the reflection (= left adjoint functor) of the natural inclusion of the category of real reduced multirings into the category of pre-ordered multirings and explore some of these properties; 
(ii) by employing sheaf-theoretic methods, we characterize the real reduced hyperrings as certain "geometric" von Neumann regular real hyperrings and describe the functor V, the "geometric" von Neumann regular hull of a multiring;
(iii) we present some interesting logical-algebraic interactions between the functors Q and V that are useful to describe the Witt ring of a real semigroup (or real reduced multiring).
AdresseSophie Germain