GORENSTEIN PROJECTIVE PRECOVERS AND FINITELY PRESENTED MODULES

Sergio Estrada, Alina Iacob

Research output: Contribution to journalArticlepeer-review

Abstract

The existence of the Gorenstein projective precovers over arbitrary rings is an open question. It is known that if the ring has finite Gorenstein global dimension, then every module has a Gorenstein projective precover. We prove here a “reduction” property — we show that, over any ring, it suffices to consider finitely presented modules: if there exists a nonnegative integer n such that every finitely presented module has Gorenstein projective dimension ≤ n, then the class of Gorenstein projective modules is special precovering.

Original languageEnglish
Pages (from-to)715-721
Number of pages7
JournalRocky Mountain Journal of Mathematics
Volume54
Issue number3
DOIs
StatePublished - Jun 2024

Keywords

  • finitely presented modules
  • Gorenstein projective dimension
  • Gorenstein projective precover

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