Finitely generated flat modules and a characterization of semiperfect rings

Alberto Facchini, Dolors Herbera, Iskhak Sakhajev

Research output: Contribution to journalArticleResearchpeer-review

14 Citations (Scopus)

Abstract

For a ring S, let K0(FGFl(S)) and K0(FGPr(S)) denote the Grothendieck groups of the category of all finitely generated flat 5-modules and the category of all finitely generated projective 5-modules respectively. We prove that a semilocal ring R is semiperfect if and only if the group homomorphism K0(FGFl(R)) → K0(FGFl(R/J(R))) is an epimorphism and K0(FGFl(R)) = K0(FGPr(R)).
Original languageEnglish
Pages (from-to)4195-4214
JournalCommunications in Algebra
Volume31
DOIs
Publication statusPublished - 1 Sep 2003

Keywords

  • Flat modules
  • Lifting idempotents
  • Semilocal rings
  • Semiperfect rings

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