Hostname: page-component-7bb8b95d7b-s9k8s Total loading time: 0 Render date: 2024-09-27T08:28:16.129Z Has data issue: false hasContentIssue false
  • English
  • Français

A generalized principal ideal theorem

Published online by Cambridge University Press:  22 January 2016

David Eisenbud  and
E. Graham Evans Jr.
David Eisenbud
Affiliation:
Dept. of Math.Brandeis University, Waltham Ma. 02166, USA
E. Graham Evans Jr.
Affiliation:
Dept. of Math.University of Illinois, Urbana, Ill. 61801
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Krull’s principal ideal theorm [Krull] states that q elements in the maximal ideal of a local noetherian ring generate an ideal whose minimal components are all of height at most q. Writing R for the ring, we may consider the q elements, x1, · · ·, xq say, as coordinates of an element x ∈ Rq.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 62 , September 1976 , pp. 41 - 53
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

[B-M] Bass, H. and Murthy, M. P.: Grothendieck Groups and Picard Groups of Abelian Group Rings, Ann. of Math. 86 (1967), 16–73.Google Scholar
[B-E] Buchsbaum, D. A. and Eisenbud, D.: What makes a complex exact? J. Alg. 13 (1973), 259–268.Google Scholar
[B-R] Buchsbaum, D. A. and Rim, D. S.: A generalized Koszul Complex II—Depth and Multiplicity, Trans. Am. Math. Soc. 111 (1964), 197–225.Google Scholar
[Ea] Eagon, J. A.: Ideals generated by subdeterminants of a matrix, Thesis, University of Chicago (1961).Google Scholar
[E-N] Eagon, J. A. and Northcott, D. G.: Ideals defined by matrices and a certain complex associated with them, Proceedings of the Royal Soc. of England A, 269 (1962), 188–204.Google Scholar
[E-E] Eisenbud, D. and Evans, E. G.: Generating modules efficiently; Theorems from algebraic K-theory, J. Alg. 27 (1973), 278–305.CrossRefGoogle Scholar
[H] Hochster, M.: Deep local rings, to appear.Google Scholar
[Kron] Kronecker, L.: Grundzüge einer arithmetischer Theorie der algebraischen Grössen, J. Reine angew. Math. 92 (1882), 1–122.Google Scholar
[Krull] Krull, W.: Über einen Hauptsatz der allgemeinen Idealtheorie, S.-B. Heidelberg Akad. Wiss. (1929), 11–16.CrossRefGoogle Scholar
[Mac] Macaulay, F. S.: The Algebraic Theory of Modular Systems, Cambridge Tracts in Mathematics and Math. Physics, 19 (1916).Google Scholar
[N] Northcott, D. G.: Semi-regular rings and semi-regular ideals, Quart. J. Math. (2) 11 (1960), 81–104.CrossRefGoogle Scholar
[P-S] Peskine, C. and Szpiro, L.: Dimension projective finie et cohomologie locale, Pub. I.H.E.S. Paris 42, 1973.CrossRefGoogle Scholar
[S] Serre, J.-P.: Algèbre Locale—Multiplicités, Springer Lecture Notes in Math. 11, 1958.Google Scholar