Let $(R,\mathfrak {m}) $ be a Noetherian local ring and $ M $, $ N $ be two finitely generated
$ R $-modules. In this paper it is shown that $ R $ is a Cohen-Macaulay ring if and only if …

ON THE PROJECTIVE DIMENSION OF ARTINIAN MODULES 1. Introduction Let R denote a
commutative Noetherian ring with identity, I be a Page 1 Journal of Algebraic Systems Vol. 9 …

Let (R, m) be a Noetherian local ring and M, N be two finitely generated R-modules. In this
paper it is shown that R is a Cohen-Macaulay ring if and only if R admits a non-zero Artinian …

Let (R, m) be a Noetherian local ring and M, N be two finitely generated R-modules. In this
paper it is shown that R is a Cohen-Macaulay ring if and only if R admits a non-zero Artinian …

Abstract Let $(R,\mathfrak {m}) $ be a Noetherian local ring and $ M $, $ N $ be two finitely
generated $ R $-modules. In this paper it is shown that $ R $ is a Cohen-Macaulay ring if …