Structures paragraduées (groupes, anneaux, modules), I

Anneaux p-Adiquement Clos et Anneaux de Fonctions Définissables

Some Properties of I-Closed Modules

Anneaux de Fonctions p-adiques

We study first-order properties of the quotient rings 9(V)/1 by a prime ideal 9, where 9( V) is the ring of p-adic valued continuous definable functions on some affine p-adic variety V. We show that they are integrally closed Henselian local rings, with a p-adically closed residue field and field of fractions, and they are not valuation rings in general but always satisfy Vx, y(x Iy2 V y IX2). ...

Global model structures for - modules

We extend Schwede’s work on the unstable global homotopy theory of orthogonal spaces and L-spaces to the category of ∗-modules (i.e., unstable S-modules). We prove a theorem which transports model structures and their properties from L-spaces to ∗-modules and show that the resulting global model structure for ∗-modules is monoidally Quillen equivalent to that of orthogonal spaces. As a conseque...

Some comments and examples on generation of (hyper-)archimedean -groups and f-rings

— This paper systematizes some theory concerning the generation of -groups and reduced f -rings from substructures. We are particularly concerned with archimedean and hyperarchimedean groups and rings. We discuss the process of adjoining a weak order unit to an -group, or an identity to an f -ring and find significant contrasts between these cases. In -groups, hyperarchimedeanness and similar p...