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R-Sequences and Homological Dimension1)

Published online by Cambridge University Press:  22 January 2016

Irving Kaplansky
Irving Kaplansky*
Affiliation:
University of Chicago
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The motivation for the results in this note comes from a theorem of Macaulay. Let f1, …, fn be elements of a polynomial ring R over a field, and let I be the ideal they generate. Assume IR and rank (I) = n. Then the theorem of Lasker and Macaulay asserts that I is unmixed (all prime ideals belonging to I have rank n). Macaulay [1, p. 51] proved further that any power of I is unmixed.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 20 , June 1962 , pp. 195 - 199
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1962

Footnotes

1)

Research supported in part by the office of ordnance Research, U. S. Army.

References

[1] Macaulay, F. S., The Algebraic Theory of Modular Systems, Cambridge, 1916.Google Scholar
[2] Rees, D., The grade of an ideal or module, Proc. Camb. Phil. Soc. 53 (1957), 28–42.Google Scholar