The Cohen Macaulay property for noncommutative rings

Brown, K. A. and Macleod, M. J. (2017) The Cohen Macaulay property for noncommutative rings. Algebras and Representation Theory, 20(6), pp. 1433-1465. (doi: 10.1007/s10468-017-9694-z)

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Let R be a noetherian ring which is a fifinite module over its centre Z(R). This paper studies the consequences for R of the hypothesis that it is a maximal Cohen Macaulay Z(R)-module. A number of new results are proved, for example projectivity over regular commutative subrings and the direct sum decomposition into equicodimensional rings in the affine case, and old results are corrected or improved. The additional hypothesis of homological grade symmetry is proposed as the appropriate extra lever needed to extend the classical commutative homological hierarchy to this setting, and results are proved in support of this proposal. Some speculations are made in the final section about how to extend the definition of the Cohen-Macaulay property beyond those rings which are finite over their centres.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Brown, Professor Ken
Authors: Brown, K. A., and Macleod, M. J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Algebras and Representation Theory
Publisher:Springer Verlag
ISSN (Online):1572-9079
Published Online:02 May 2017
Copyright Holders:Copyright © 2017 The Authors
First Published:First published in Algebras and Representation Theory 20(6):1433-1465
Publisher Policy:Reproduced under a Creative Commons License

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