Proposition 15.50.12. The following types of rings are G-rings:
fields,
Noetherian complete local rings,
\mathbf{Z},
Dedekind domains with fraction field of characteristic zero,
finite type ring extensions of any of the above.
Proposition 15.50.12. The following types of rings are G-rings:
fields,
Noetherian complete local rings,
\mathbf{Z},
Dedekind domains with fraction field of characteristic zero,
finite type ring extensions of any of the above.
Proof. For fields, \mathbf{Z} and Dedekind domains of characteristic zero this follows immediately from the definition and the fact that the completion of a discrete valuation ring is a discrete valuation ring. A Noetherian complete local ring is a G-ring by Proposition 15.50.6. The statement on finite type overrings is Proposition 15.50.10. \square
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