Kaplansky classes, finite character and aleph(1)-projectivity

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10128138" target="_blank" >RIV/00216208:11320/12:10128138 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1515/FORM.2011.101" target="_blank" >http://dx.doi.org/10.1515/FORM.2011.101</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/FORM.2011.101" target="_blank" >10.1515/FORM.2011.101</a>

Result language

angličtina

Original language name

Kaplansky classes, finite character and aleph(1)-projectivity

Original language description

Kaplansky classes emerged in the context of Enochs' solution of the Flat Cover Conjecture. Their connection to abstract model theory goes back to Baldwin et al.: a class C of roots of Ext is a Kaplansky class closed under direct limits if and only if thepair (C, {=) is an abstract elementary class (AEC) in the sense of Shelah. We prove that this AEC has finite character in case C = C-perpendicular to' for a class C' of pure-injective modules. In particular, all AECs of roots of Ext over any right noetherian right hereditary ring R have finite character (but the case of general rings remains open). If (C, {=) is an AEC of roots of Ext, then C is known to be a covering class. However, Kaplansky classes need not even be precovering in general: We prove that the class D of all aleph(1)-projective modules (which is equal to the class of all flat Mittag-Leffler modules) is a Kaplansky class for any ring R, but it fails to be precovering in case R is not right perfect, the class (perpendicul

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2012

Confidentiality

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

Name of the periodical

Forum Mathematicum

ISSN

0933-7741

e-ISSN

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Volume of the periodical

24

Issue of the periodical within the volume

5

Country of publishing house

DE - GERMANY

Number of pages

19

Pages from-to

1091-1109

UT code for WoS article

000309161800008

EID of the result in the Scopus database

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