Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T23:55:51.164Z Has data issue: false hasContentIssue false

On Northcott-Rees theorem on principal systems

Published online by Cambridge University Press:  22 January 2016

Yuji Yoshino*
Affiliation:
Faculty of Integrated Arts and Sciences, Hiroshima University, Hiroshima, 730, Japan
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.

Let R be a local ring with maximal ideal m and let us make the following definition according to the paper [NR] of Northcott and Rees, which is essentially due to F. S. Macaulay.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

Aoyama, Y., Some basic results on canonical modules, J. Math. Kyoto Univ., 23 no. 1 (1983), 8594.Google Scholar
Ferrand, D. and Raynaud, M., Fibres formelles d’un anneau local noethérien, Ann. Sci. École Norm. Sup. (4), t. 3 (1970), 295311.CrossRefGoogle Scholar
Hochster, M., Cyclic purity versus purity in excellent Noetherian rings, Trans. Amer. Math. Soc, 231 no. 2 (1977), 463488.Google Scholar
Herzog, J. Kunz, E. et al., Der kanonische Modul eines Cohen-Macaulay Rings, Lect. Notes in Math., 238, Springer Verlag, (1971).Google Scholar
Matlis, E., Injective modules over Noetherian rings, Pacific J. Math., 8 (1958), 511528.Google Scholar
Nagata, M., Local Rings, Interscience Tracts in Pure and Applied Math., 13, J. Wiley, New York, 1962.Google Scholar
[NR] Northcott, D. G. and Rees, D., Principal systems, Quart. J. Math. Oxford (2), 8 (1957), 119127.Google Scholar
[R] Ratliff, L.J., On quasi-unmixed local domains, the altitude formula, and the chain condition for prime ideals (I), Amer. J. Math., 91 (1969), 508528.Google Scholar
[S] Sharp, R.Y., Acceptable rings and homomorphic images of Gorenstein rings, J. Algebra, 44 (1977), 246261.Google Scholar
[S2] Sharp, R.Y., A commutative Noetherian rings which possesses a dualizing complex is acceptable, Math. Proc. Cambridge Philos. Soc, 82 (1977), 197213.Google Scholar