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Matthias Schötz: Rings of almost everywhere defined functions

Datum objave: 11. 10. 2024
Seminar za algebro in funkcionalno analizo
četrtek
17
oktober
Ura:
12.30 - 13.30
Lokacija:
FMF, Jadranska 21, predavalnica 2.03

Abstract:

I will present the following representation theorem and some applications: A partially ordered commutative ring R is a subring of a ring of almost everywhere defined continuous real-valued functions on a compact Hausdorff space X if and only if R is archimedean and localizable. Here we assume that the positive cone of R is closed under multiplication and stable under multiplication with squares, but actually one of these assumptions implies the other. An almost everywhere defined function on X is one that is defined on a dense open subset of X. A partially ordered commutative ring R is archimedean if the underlying additive partially ordered abelian group is archimedean, and R is localizable essentially if its order is compatible with the construction of a localization with sufficiently large, positive denominators. This talk is based on arXiv preprint 2406.13063.

Vljudno vabljeni.

Roman Drnovšek in Primož Moravec