G-ring

In commutative algebra, a G-ring or Grothendieck ring is a Noetherian ring such that the map of any of its local rings to the completion is regular (defined below). Almost all Noetherian rings that occur naturally in algebraic geometry or number theory are G-rings, and it is quite hard to construct examples of Noetherian rings that are not G-rings. The concept is named after Alexander Grothendieck.

For the Saturn G ring, see Rings of Saturn.

A ring that is both a G-ring and a J-2 ring is called a quasi-excellent ring, and if in addition it is universally catenary it is called an excellent ring.

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