Reconstructing projective modules from its trace ideal

Dolors Herbera, Pavel Příhoda

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)


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. © 2014 Elsevier Inc.
Original languageEnglish
Pages (from-to)25-57
JournalJournal of Algebra
Publication statusPublished - 15 Oct 2014


  • FCR-algebras
  • Idempotent ideal
  • Primary
  • Projective modules
  • Ring
  • Trace ideal


Dive into the research topics of 'Reconstructing projective modules from its trace ideal'. Together they form a unique fingerprint.

Cite this