What is the Rees algebra of a module
By David Eisenbud, Craig Huneke, Bernd Ulrich. 2002
93 citations recorded by the source corpus.
In this paper we show that the Rees algebra can be made into a functor on modules over a ring in a way that extends its classical definition for ideals. The Rees algebra of a module M may be computed in terms of a maximal map f from M to a free module as the image of the map induced by f on symmetric algebras. We show that the analytic spread and reductions of M can be determined from any embedding of M into a free module, and in characteristic 0-but not in positive characteristic!-the Rees algebra itself can be computed from any such embedding.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/ac4feabf7460e22fb2509c2e5f6f9838124adcdb
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In Algebra and Number Theory
In Geometry and Topology
Citations in the corpus
- Integral closure of ideals, rings, and modules (2006, methodology): “This was first done by Zariski and Samuel for modules contained in overfields in [324, Appendix 4], and later extended to general modules by Rees in [241] and even later by Eisenbud, Huneke and Ulrich [69].”