Characterizing local rings via complete intersection homological dimensions

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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 finite projective dimension or a nonzero finitely generated R-module of finite 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.