Document Type : Original Manuscript

Authors

• A. Mafi ¹
• S. Tabejamaat ²

¹ Department of Mathematics, University of Kurdistan, P.O.Box 416, Sanandaj, Iran.

² Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.

Abstract

Let $(R,\underline{m})$ be a commutative Noetherian local ring and $M$ be a non-zero finitely generated $R$-module. We show that if $R$ is almost Cohen-Macaulay and $M$ is perfect with finite projective dimension, then $M$ is an almost Cohen-Macaulay module. Also, we give some necessary and sufficient condition on $M$ to be an almost Cohen-Macaulay module, by using $\Ext$ functors.

Keywords

• Almost Cohen-Macaulay modules
• Cohen-Macaulay modules
• Ext functors