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The syzygies of m-full ideals

Published online by Cambridge University Press:  24 October 2008

Junzo Watanabe
Junzo Watanabe
Affiliation:
Hokkaido Tokai University, Department of Mathematics, Minami-ku, Sapporo 005, Japan
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Extract

The concept of an m-full ideal was introduced and studied first by D. Rees (unpublished). In 1983, after having considered and discussed the concept with Professor Rees, the author showed some properties of these ideals in [11], and other authors also have obtained results related to them (cf. [5, 7]). The purpose of this paper is to seek syzygies of m-full ideals and try to analyze their structure. Let a be an m-full ideal, and ᾱ the reduction by a general element. Then it is possible to determine the number of basic syzygies of a in terms of ᾱ. We show that this leads to a method for obtaining a set of basic syzygies of a provided that one for ᾱ is known (Theorem 6). Moreover the entire structure of the syzygy module is known when it is reduced by a general element. It turns out that a/za is the direct sum of ᾱ and copies of the residue field (Corollary 7).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 109 , Issue 1 , January 1991 , pp. 7 - 13
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

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