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Lower and upper bounds for Cohen-Macaulay dimension

Published online by Cambridge University Press:  17 April 2009

J. Asadollahi  and
Sh. Salarain
J. Asadollahi
Affiliation:
Institute for Studies in Theoretical Physics andMathematics, P.O.Box 19395-5746, Tehran, Iran and Faculty of Science, Shahre-Kord University, P.O.Box 115, Shahre-Kord, Iran e-mail: Asadollahi@ipm.ir
Sh. Salarain
Affiliation:
School of Mathematics Institute for studies in Theoretical Physics and Mathematics (IPM), P.O.Box: 19395-5746, Tehran, Iran and Department of Mathematics, University of Isfahan, P.O. Box 81746-73441, IsfahanIran e-mail: Salarian@ipm.ir
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Lower and upper bounds for CM-dimension, called CM*-dimension and CM*-dimension, will be defined for any finitely generated module M over a local Noetherian ring R. Both CM* and CM*-dimension reflect the Cohen–Macaulay property of rings. Our results will show that these dimensions have the expected basic properties parallel to those of the homological dimensions. In particular, they satisfy an analog of the Auslander-Buchsbaum formula.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 2 , April 2005 , pp. 337 - 346
Copyright
Copyright © Australian Mathematical Society 2005

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