Reductions and special parts of closures

Details Reductions and special parts of closures Reductions and special parts of closures

2010-02-13

arxiv.org/abs/1002.2703v2

Journal of Algebra, Volume 323, Issue 8, 15 April 2010, pp. 2209-2225.

Mathematics

Commutative Algebra

to appear in Journal of Algebra (This version corrects some typos)

Scientific paper

10.1016/j.jalgebra.2010.02.015

We provide an axiomatic framework for working with a wide variety of closure
operations on ideals and submodules in commutative algebra, including notions
of reduction, independence, spread, and special parts of closures. This
framework is applied to tight, Frobenius, and integral closures. Applications
are given to evolutions and special Brian\c{c}on-Skoda theorems.

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