About: Reconstructing projective modules from its trace ideal

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://dx.doi.org/10.1016/j.jalgebra.2014.06.010
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 right ideals. 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 classification results 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. 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 right ideals. 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 classification results 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. (en)
Title	Reconstructing projective modules from its trace ideal Reconstructing projective modules from its trace ideal (en)
skos:prefLabel	Reconstructing projective modules from its trace ideal Reconstructing projective modules from its trace ideal (en)
skos:notation	RIV/00216208:11320/14:10287253!RIV15-MSM-11320___
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GA201/09/0816), P(GBP201/12/G028)
http://linked.open...iv/cisloPeriodika	2014
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Příhoda, Pavel
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	41625
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/14:10287253
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Idempotent ideal; FCR-algebras; Trace ideal; Projective modules; Ring (en)
http://linked.open.../riv/klicoveSlovo	Ring FCR-algebras Idempotent ideal Projective modules Trace ideal
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[6F50C4A84DB8]
http://linked.open...i/riv/nazevZdroje	Journal of Algebra
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Eduard Čech Institute for algebra, geometry and mathematical physics Algebraické metody teorie reprezentací (aproximace, realizace a omezení)
http://linked.open...UplatneniVysledku	2014
http://linked.open...v/svazekPeriodika	416
http://linked.open...iv/tvurceVysledku	Příhoda, Pavel Herbera, D.
http://linked.open...ain/vavai/riv/wos	000339696400002
issn	0021-8693
number of pages	33 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.jalgebra.2014.06.010
http://localhost/t...ganizacniJednotka	11320

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