R-Sequences and Homological Dimension
- 1 June 1962
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 20, 195-199
- https://doi.org/10.1017/s0027763000023710
Abstract
The motivation for the results in this note comes from a theorem of Macaulay. Let f 1, …, fn be elements of a polynomial ring R over a field, and let I be the ideal they generate. Assume I R 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.Keywords
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