Abstract
This paper gives a change of rings theorem for homological dimensions which seems especially suited for the study of the commutative rings of global dimension two. Elsewhere we gave a description of the local rings of global dimension two that when applied to the global case yields an idea of what the spectrum of such rings look like "down" from a maximal ideal. Here an attempt is made to describe the spectrum "up" from a minimal prime ideal.
Keywords
- Prime Ideal
- Spectral Sequence
- Local Ring
- Maximal Ideal
- Commutative Ring
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Partially supported by National Science Foundation Grant GP-19995.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
M. Auslander and D. Buchsbaum, Codimension and Multiplicity, Annals Math. 68 (1958), 625–657.
H. Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans.Amer.Math.Soc. 95 (1960), 466–488.
N. Bourbaki, Algèbre Commutative, Hermann, Paris, 1961–65.
L. Burch, On ideals of finite homological dimension in local rings, Proc.Camb.Phil.Soc. 64 (1968), 941–948.
H.Cartan and S.Eilenberg, Homological Algebra, Princeton University Press, 1956.
S.U. Chase, Direct product of modules, Trans. Amer.Math.Soc. 97 (1960), 457–473.
J.M. Cohen, A note on homological dimension, J.Algebra 11 (1969), 483–487.
L. Gruson and M. Raynaud, Critères de platitude et de projectivité, Inventines Math. 13 (1971), 1–89.
W. Heinzer and J. Ohm, Locally noetherian commutative rings, Trans. Amer. Math.Soc. 158 (1971), 273–284.
C.U. Jensen, Some remarks on a change of rings theorem, Math. Zeit. 106 (1968), 395–401.
I. Kaplansky, Commutative Rings, Allyn and Bacon, Boston, 1970.
_____, Fields and Rings, University of Chicago Press, 1969.
R.E. MacRae, On an application of the Fitting invariants, J. Algebra 2 (1965), 153–169.
W.V. Vasconcelos, On projective modules of finite rank, Proc. Amer.Math.Soc. 22 (1969), 430–433.
____, Annihilators of modules with a finite free resolution, Proc.Amer.Math.Soc. 29 (1971), 440–442.
_____, Finiteness in projective ideals, J.Algebra (to appear).
_____, The local rings of global dimension two, Proc. Amer.Math.Soc. (to appear).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1973 Springer-Verlag
About this paper
Cite this paper
Vasconcelos, W.V. (1973). Rings of global dimension two. In: Brewer, J.W., Rutter, E.A. (eds) Conference on Commutative Algebra. Lecture Notes in Mathematics, vol 311. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068933
Download citation
DOI: https://doi.org/10.1007/BFb0068933
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06140-3
Online ISBN: 978-3-540-38340-6
eBook Packages: Springer Book Archive
