# Seminario MALGA Padova Verona - Moduli Algebre Anelli: “Cotorsion modules over Noetherian commutative rings of Krull dimension 1”

## Martedì 11 Aprile 2017, ore 11:30 - Aula 1BC45 - Leonid Positselki

ARGOMENTI: Seminari

Martedì 11 Aprile 2017 alle ore 11:30 in Aula 1BC45, Leonid Positselki (University of Haifa and Institute for Information Transmission Problems, Moscow) terrà un seminario dal titolo “Cotorsion modules over Noetherian commutative rings of Krull dimension 1“, nell'ambito del Seminario Padova-Verona MALGA - Moduli Algebre Anelli.

Abstract
I will explain how to extend the theory of almost perfect domains to arbitrary Noetherian commutative rings $R$ of Krull dimension 1, by showing that an $R$-module is cotorsion if and only if it is $Ext^1$-orthogonal to $S^{-1}R$, where $S$ is the complement to the union of all minimal prime ideals in $R$. The proof uses the theory of contramodules over a commutative ring with a fixed ideal, and the two-term complex $R \to S^{-1}R$ in place of the traditional quotient module $S^{-1}R/R$.