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A note on grade

Published online by Cambridge University Press:  22 January 2016

P. Jothilingam
P. Jothilingam*
Affiliation:
Tata Institute of Fundamental Research
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All rings that occur in this note will be assumed to be commutative with unity and all modules will be finitely generated and unitary.

The grade of a module M over a noetherian local ring R is defined to be the length of a maximal R-sequence contained in the annihilator of M. If M has finite projective dimension it is well-known that grade M ≤ proj. dim M. We can say more when R is a regular local ring.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 59 , December 1975 , pp. 149 - 152
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

References

[1] Auslander, M. and Goldman, 0.: Maximal order, Trans. Amer. Math. Soc. Vol. 97(1960).CrossRefGoogle Scholar
[2] Auslander, M.: On the purity of the branch locus, American Journal of Mathematics Vol. 84 (1962).CrossRefGoogle Scholar
[3] Auslander, M.: Coherent functors, Proceedings of a conference on categorical algebra, La Jolla 1965, Springer-Verlag Berlin, Heidelberg, New York 1966.Google Scholar
[4] Ischebeck, F.: Eine Dualitat zwischen den Funktoren Ext und Tor, J. Algebra 11 (1969), 510–531.Google Scholar
[5] Rees, D.: The grade of an ideal or module, Proc. Camb. Phil. Soc. 53 (1957).CrossRefGoogle Scholar
[6] Lichtenbaum, S.: On the vanishing of Tor in regular local rings Illinois. J. of Math. Vol. 10 (1966).Google Scholar