Kommutativer noetherscher Ring/Lokal/Parameterrealisierung/Fakt

Es sei ${}(R,{\mathfrak {m}})$ ein noetherscher lokaler Ring der Dimension ${}d$ .

Dann gibt es Elemente ${}f_{1},\ldots ,f_{d}\in {\mathfrak {m}}$ mit

${}\operatorname {rad} {\left(f_{1},\ldots ,f_{d}\right)}={\mathfrak {m}}\,.$

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