Open AccessAn elementary proof of the Briançon-Skoda theorem
Author(s) -
Jacob Sznajdman
Publication year - 2011
Publication title -
annales de la faculté des sciences de toulouse mathématiques
Language(s) - English
Resource type - Journals
eISSN - 2258-7519
pISSN - 0240-2963
DOI - 10.5802/afst.1262
Subject(s) - ideal (ethics) , mathematics , closure (psychology) , elementary proof , ring (chemistry) , square (algebra) , pure mathematics , function (biology) , combinatorics , discrete mathematics , geometry , philosophy , law , chemistry , political science , organic chemistry , epistemology , evolutionary biology , biology
We give a new elementary proof of the Brian\c{c}on-Skoda theorem, whichstates that for an $m$-generated ideal $\mathfrak{a}$ in the ring of germs ofanalytic functions at $0\in \C^n$, the $\nu$:th power of its integral closureis contained in $\mathfrak{a}$, where $\nu = \min(m,n)$.
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