Mafi, A., Tabejamaat, S. (2015). RESULTS ON ALMOST COHEN-MACAULAY MODULES. Journal of Algebraic Systems, 3(2), 147-150. doi: 10.22044/jas.2015.614
A. Mafi; S. Tabejamaat. "RESULTS ON ALMOST COHEN-MACAULAY MODULES". Journal of Algebraic Systems, 3, 2, 2015, 147-150. doi: 10.22044/jas.2015.614
Mafi, A., Tabejamaat, S. (2015). 'RESULTS ON ALMOST COHEN-MACAULAY MODULES', Journal of Algebraic Systems, 3(2), pp. 147-150. doi: 10.22044/jas.2015.614
Mafi, A., Tabejamaat, S. RESULTS ON ALMOST COHEN-MACAULAY MODULES. Journal of Algebraic Systems, 2015; 3(2): 147-150. doi: 10.22044/jas.2015.614
1Department of Mathematics, University of Kurdistan, P.O.Box 416, Sanandaj, Iran.
2Department 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.
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