2002/09/15 by David Eisenbud, Eisenbud, David, Craig Huneke +3 · 1 citation
Computer Science · Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #Polynomial and algebraic computation #math.AC #math.AG #msc:13B21 #msc:13C12 #msc:13C15
paper · pdf · doi:10.48550/arxiv.math/0209187
8 pages, AMS-TeX. Accepted 8/2001 for the Proceedings of the American Mathematical Society
arxiv created 2002/09/15 · arxiv updated 2009/11/30
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. It is 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.