Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-05T21:39:07.135Z Has data issue: false hasContentIssue false
  • English
  • Français

A common generalization of local cohomology theories

Published online by Cambridge University Press:  18 May 2009

M. H. Bijan-Zadeh
M. H. Bijan-Zadeh
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH.
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.

Throughout this note all rings considered will be commutative and noetherian and will have non-zero identity elements. A will always denote such a ring and the category of all A-modules and all A-homomorphisms will be denoted by A.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 21 , Issue 1 , January 1980 , pp. 173 - 181
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980

References

REFERENCES

1.Bănică, C. and Stoia, M., Singular sets of a module and local cohomology, National Institute for Scientific and Technical Creation/Institute of Mathematics, Bucharest, preprint.Google Scholar
2.Bijan-Zadeh, M. H., Torsion theories and local cohomology over commutative noetherian rings, J. London Math. Soc. (2) 19 (1979), 402–410.CrossRefGoogle Scholar
3.Cartan, H. and Eilenberg, S., Homological algebra (Princeton University Press, 1956).Google Scholar
4.Eilenberg, S. and Steenrod, N., Foundations of algebraic topology (Princeton University Press, 1952).CrossRefGoogle Scholar
5.Grothendieck, A., Local cohomology, Lecture Notes in Mathematics 41 (Springer-Verlag, 1967).Google Scholar
6.Herzog, J., Komplexe, Auflösungen und dualität in der Lokalen Algebra, preprint, Universität Essen.Google Scholar
7.Northcott, D. G., An introduction to homological algebra (Cambridge University Press, 1960).CrossRefGoogle Scholar
8.Northcott, D. G., Lessons on rings, modules and multiplicities (Cambridge University Press, 1968).CrossRefGoogle Scholar
9.Sharp, R. Y., Local cohomology theory in commutative algebra, Quart. J. Math. Oxford (2) 21 (1970), 425–434.CrossRefGoogle Scholar
10.Sharp, R. Y., Gorenstein modules, Math. Z. 115 (1970), 117–139.CrossRefGoogle Scholar
11.Sharp, R. Y., Ramification indices and injective modules, J. London Math. Soc. (2) 11 (1975), 267–275.Google Scholar
12.Suzuki, N., On the generalized local cohomology and its duality, J. Math. Kyoto Univ. 18 (1978), 71–85.Google Scholar