Specialization and Integral Closure

Details Specialization and Integral Closure Specialization and Integral Closure

2006-11-25

arxiv.org/abs/math/0611773v1

Mathematics

Commutative Algebra

20 pages

Scientific paper

In this paper we prove in a rather general setting that the integral closure of ideals and modules is preserved under specialization modulo generic elements. One of the main results, Theorem 2.1, can be paraphrased by saying that an element is integral over an ideal if it is integral modulo a generic element of the ideal. Another set of applications of our main theorem concerns integral closures of modules. The significance of Theorem 4.5 is that it turns questions about integral closures of modules into problems about integral closures of ideals, by means of a construction known as Bourbaki ideals.

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