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A common generalization of local cohomology theories

  • M. H. Bijan-Zadeh (a1)
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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.

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COPYRIGHT: © Glasgow Mathematical Journal Trust 1980
References
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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.
2.Bijan-Zadeh, M. H., Torsion theories and local cohomology over commutative noetherian rings, J. London Math. Soc. (2) 19 (1979), 402–410.
3.Cartan, H. and Eilenberg, S., Homological algebra (Princeton University Press, 1956).
4.Eilenberg, S. and Steenrod, N., Foundations of algebraic topology (Princeton University Press, 1952).
5.Grothendieck, A., Local cohomology, Lecture Notes in Mathematics 41 (Springer-Verlag, 1967).
6.Herzog, J., Komplexe, Auflösungen und dualität in der Lokalen Algebra, preprint, Universität Essen.
7.Northcott, D. G., An introduction to homological algebra (Cambridge University Press, 1960).
8.Northcott, D. G., Lessons on rings, modules and multiplicities (Cambridge University Press, 1968).
9.Sharp, R. Y., Local cohomology theory in commutative algebra, Quart. J. Math. Oxford (2) 21 (1970), 425–434.
10.Sharp, R. Y., Gorenstein modules, Math. Z. 115 (1970), 117–139.
11.Sharp, R. Y., Ramification indices and injective modules, J. London Math. Soc. (2) 11 (1975), 267–275.
12.Suzuki, N., On the generalized local cohomology and its duality, J. Math. Kyoto Univ. 18 (1978), 71–85.
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