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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F14%3A10287253%21RIV15-MSM-11320___
rdf:type
n13:Vysledek skos:Concept
rdfs:seeAlso
http://dx.doi.org/10.1016/j.jalgebra.2014.06.010
dcterms: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.
dcterms:title
Reconstructing projective modules from its trace ideal Reconstructing projective modules from its trace ideal
skos:prefLabel
Reconstructing projective modules from its trace ideal Reconstructing projective modules from its trace ideal
skos:notation
RIV/00216208:11320/14:10287253!RIV15-MSM-11320___
n3:aktivita
n10:P n10:I
n3:aktivity
I, P(GA201/09/0816), P(GBP201/12/G028)
n3:cisloPeriodika
2014
n3:dodaniDat
n5:2015
n3:domaciTvurceVysledku
n18:4326865
n3:druhVysledku
n11:J
n3:duvernostUdaju
n19:S
n3:entitaPredkladatele
n20:predkladatel
n3:idSjednocenehoVysledku
41625
n3:idVysledku
RIV/00216208:11320/14:10287253
n3:jazykVysledku
n16:eng
n3:klicovaSlova
Idempotent ideal; FCR-algebras; Trace ideal; Projective modules; Ring
n3:klicoveSlovo
n9:Ring n9:Trace%20ideal n9:Projective%20modules n9:FCR-algebras n9:Idempotent%20ideal
n3:kodStatuVydavatele
US - Spojené státy americké
n3:kontrolniKodProRIV
[6F50C4A84DB8]
n3:nazevZdroje
Journal of Algebra
n3:obor
n6:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n4:GBP201%2F12%2FG028 n4:GA201%2F09%2F0816
n3:rokUplatneniVysledku
n5:2014
n3:svazekPeriodika
416
n3:tvurceVysledku
Příhoda, Pavel Herbera, D.
n3:wos
000339696400002
s:issn
0021-8693
s:numberOfPages
33
n8:doi
10.1016/j.jalgebra.2014.06.010
n17:organizacniJednotka
11320