Reconstructing projective modules from its trace ideal
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10287253" target="_blank" >RIV/00216208:11320/14:10287253 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jalgebra.2014.06.010" target="_blank" >http://dx.doi.org/10.1016/j.jalgebra.2014.06.010</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jalgebra.2014.06.010" target="_blank" >10.1016/j.jalgebra.2014.06.010</a>
Alternative languages
Result language
angličtina
Original language name
Reconstructing projective modules from its trace ideal
Original language description
We make a detailed study of idempotent ideals that are traces of countably generated projective right modules. We associate to such ideals an ascending chain of finitely generated left ideals and, dually, a descending chain of cofinitely generated rightideals. The study of the first sequence allows us to characterize trace ideals of projective modules and to show that projective modules can always be lifted modulo the trace ideal of a projective module. As a consequence we give some new classificationresults of (countably generated) projective modules over particular classes of semilocal rings. The study of the second sequence leads us to consider projective modules over noetherian FCR-algebras; we make some constructions of non-trivial projective modules showing that over such rings the behavior of countably generated projective modules that are not direct sum of finitely generated ones is, in general, quite complex.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Algebra
ISSN
0021-8693
e-ISSN
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Volume of the periodical
416
Issue of the periodical within the volume
2014
Country of publishing house
US - UNITED STATES
Number of pages
33
Pages from-to
25-57
UT code for WoS article
000339696400002
EID of the result in the Scopus database
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