Characterizing local rings via complete intersection homological dimensions

Let (R, m) be a commutative Noetherian local ring. It is known that R is Cohen-Macaulay if there exists either a nonzero Cohen-Macaulay R-module of fi nite projective dimension or a nonzero fi nitely generated R-module of fi nite injective dimension. In this article, we will prove the complete intersection analogues of these facts. Also, by using complete intersection homological dimensions, we will characterize local rings which are either regular, complete intersection or Gorenstein.