Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-14T18:14:47.579Z Has data issue: false hasContentIssue false
  • English
  • Français

Pseudo-Noetherian Rings

Published online by Cambridge University Press:  20 November 2018

Kenneth P. McDowell
Kenneth P. McDowell*
Affiliation:
Department of Mathematics, McMaster University Hamilton, Ontario, CanadaL8S 4K1
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.

In the latter part of the 1950’s some interesting papers appeared (e.g. [2] and [10]) which examined the relationships occurring between the purely algebraic and homological aspects of the theory of finitely generated modules over Noetherian rings. Many of these relationships remain valid if one considers the much wider class of rings determined by the following definition.

Definition. A commutative ring R is called pseudo-Noetherian if it satisfies the following two conditions.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 1 , 01 March 1976 , pp. 77 - 84
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Auslander, M. and Bridger, M., Stable module theory, Mem. Amer. Math. Soc. 94 (1969).Google Scholar
2. Auslander, M. and Buchsbaum, D., Homological dimension in local rings, Trans. Amer. Math. Soc. 85 (1957), 390–405.Google Scholar
3. Bass, H., Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466–488.Google Scholar
4. Bourbaki, N., Éléments de Mathématique XXVII Algèbre Commutative, Hermann, Paris, 1961.Google Scholar
5. Cartan, H. and Eilenberg, S., Homological Algebra, Princeton University Press, Princeton, 1956.Google Scholar
6. Chase, S. U., Direct products of modules, Trans. Amer. Math. Soc. 97 (1960), 457–473.Google Scholar
7. Evans, E. G. Jr, Zero divisors in Noetherian-like rings, Trans. Amer. Math. Soc. 155 (1971), 505–512.Google Scholar
8. Kaplansky, I., Commutative Rings, Allyn and Bacon, Boston, 1970.Google Scholar
9. Osofsky, B. L., Upper bounds on homological dimension, Nagoya Math. J. 32 (1968), 315–322.Google Scholar
10. Rees, D., The grade of an ideal or module, Proc. Cambridge Philos. Soc. 53 (1957), 28–42.Google Scholar
11. Soublin, J. P., Anneaux et modules cohérents, J. Algebra 15 (1970), 455–472.Google Scholar
12. Vasconcelos, W. V., The local rings of global dimension two, Proc. Amer. Math. Soc. 35 (1972), 381–386.Google Scholar