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Derived functors of the torsion functor and local cohomology of noncommutative rings

Part of: Commutative algebra: Homological methods Homological algebra Abelian categories

Published online by Cambridge University Press:  09 April 2009

Jonathan S. Golan  and
Jacques Raynaud
Jonathan S. Golan
Affiliation:
Department of MathematicsUniversity of Haifa31999 Haifa, Israel
Jacques Raynaud
Affiliation:
Départment de MathématiquesUniversité Claude-Bernard(Lyon I) 69622 Villeurbanne Cedex, France
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Abstract

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Let R be an associative ring which is not necessarily commutative. For any torsion theory τ on the category of left R-modules and for any nonnegative integer n we define and study the notion of the nth local cohomology functor with respect to τ. For suitably nice rings a bound for the nonvanishing of these functors is given in terms of the τ-dimension of the modules.

MSC classification

Secondary: 18E25: Derived functors and satellites 18G10: Resolutions; derived functors 13D03: (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) 18E40: Torsion theories, radicals
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 2 , October 1983 , pp. 162 - 177
Copyright
Copyright © Australian Mathematical Society 1983

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