Projectively coresolved Gorenstein flat and ding projective modules

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12 Scopus citations

Abstract

We give necessary and sufficient conditions in order for the class of projectively coresolved Gorenstein flat modules, (Formula presented.) (respectively that of projectively coresolved Gorenstein (Formula presented.) flat modules, (Formula presented.)), to coincide with the class of Ding projective modules ((Formula presented.) We show that (Formula presented.) if and only if every Ding projective module is Gorenstein flat. This is the case if the ring R is coherent for example. We include an example to show that the coherence is a sufficient, but not a necessary condition in order to have (Formula presented.) We also show that (Formula presented.) over any ring R of finite weak Gorenstein global dimension (this condition is also sufficient, but not necessary). We prove that if the class of Ding projective modules, (Formula presented.) is covering then the ring R is perfect. And we show that, over a coherent ring R, the converse also holds. We also give necessary and sufficient conditions in order to have (Formula presented.) where (Formula presented.) is the class of Gorenstein projective modules.

Original languageEnglish
Pages (from-to)2883-2893
Number of pages11
JournalCommunications in Algebra
Volume48
Issue number7
DOIs
StatePublished - Jul 2 2020

Keywords

  • Ding projective modules
  • Gorenstein -flat modules
  • Gorenstein projective modules
  • projectively coresolved Gorenstein -flat modules

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