# Seminario MALGA Padova Verona - Moduli Algebre Anelli: The ordered K-series for a ring + Model approximations for relative homological algebra

## Giovedì 19 Marzo 2015, ore 15:00 - Aula 1BC45 - Peter Vamos + Simone Virili

ARGOMENTI: Seminari

Giovedì 19 marzo 2015 in Aula 1BC45 si terrà un incontro del Seminario Padova - Verona MALGA Moduli Algebre Anelli

ore 15:00
Peter Vamos (Exeter University)
"The ordered K-series for a ring"
Abstract
The ordered K-group of a (module) category is the universal partially ordered group for the additive and non-negative invariants on that category. Additionally it not only encapsulates these invariants but induces both a descending and an ascending chain of subcategories indexed by ordinal numbers. This way it also yields a dimension which is an ordinal number. This generalises the Gabriel-Rentschler Krull dimension when the staring category is the Serre category generated by the finitely generated modules; for example, unlike the Gabriel-Rentschler Krull dimension, it can assign the (correct) dimension to non-discrete valuation rings. When the category is that of modules with finite free resolution then this dimension behaves like grade.

ore 16:30