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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

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

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

  • 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