FLAT RING EPIMORPHISMS AND UNIVERSAL LOCALIZATIONS OF COMMUTATIVE RINGS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10436809" target="_blank" >RIV/00216208:11320/21:10436809 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=X_C4NhGqYv" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=X_C4NhGqYv</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1093/qmath/haaa041" target="_blank" >10.1093/qmath/haaa041</a>

Jazyk výsledku

angličtina

Název v původním jazyce

FLAT RING EPIMORPHISMS AND UNIVERSAL LOCALIZATIONS OF COMMUTATIVE RINGS

Popis výsledku v původním jazyce

We study different types of localizations of a commutative noetherian ring. More precisely, we provide criteria to decide: (a) if a given flat ring epimorphism is a universal localization in the sense of Cohn and Schofield; and (b) when such universal localizations are classical rings of fractions. In order to find such criteria, we use the theory of support and we analyse the specialization closed subset associated to a flat ring epimorphism. In case the underlying ring is locally factorial or of Krull dimension one, we show that all flat ring epimorphisms are universal localizations. Moreover, it turns out that an answer to the question of when universal localizations are classical depends on the structure of the Picard group. We furthermore discuss the case of normal rings, for which the divisor class group plays an essential role to decide if a given flat ring epimorphism is a universal localization. Finally, we explore several (counter)examples which highlight the necessity of our assumptions.

Název v anglickém jazyce

FLAT RING EPIMORPHISMS AND UNIVERSAL LOCALIZATIONS OF COMMUTATIVE RINGS

Popis výsledku anglicky

We study different types of localizations of a commutative noetherian ring. More precisely, we provide criteria to decide: (a) if a given flat ring epimorphism is a universal localization in the sense of Cohn and Schofield; and (b) when such universal localizations are classical rings of fractions. In order to find such criteria, we use the theory of support and we analyse the specialization closed subset associated to a flat ring epimorphism. In case the underlying ring is locally factorial or of Krull dimension one, we show that all flat ring epimorphisms are universal localizations. Moreover, it turns out that an answer to the question of when universal localizations are classical depends on the structure of the Picard group. We furthermore discuss the case of normal rings, for which the divisor class group plays an essential role to decide if a given flat ring epimorphism is a universal localization. Finally, we explore several (counter)examples which highlight the necessity of our assumptions.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA17-23112S" target="_blank" >GA17-23112S: Strukturní teorie reprezentací algeber (lokalizace a vychylující teorie)</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Quarterly Journal of Mathematics

ISSN

0033-5606

e-ISSN

—

Svazek periodika

2020

Číslo periodika v rámci svazku

71

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

32

Strana od-do

1489-1520

Kód UT WoS článku

000600666500013

EID výsledku v databázi Scopus

2-s2.0-85100012681