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What (who) is G-ring - definition
G-ring
NOETHERIAN COMMUTATIVE RING SUCH THAT THE MAP OF ANY OF ITS LOCAL RINGS TO THE COMPLETION IS REGULAR
Grothendieck ring; Regular morphism; Regular homomorphism
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.
Bague
 h. Nałęcz ring 2.png?width=200 "120px")
.jpg?width=200 "120px")
![The fictional [[One Ring]]](https://commons.wikimedia.org/wiki/Special:FilePath/One Ring Blender Render.png?width=200 "The fictional [[One Ring]]")
![bezel]], and 4) stone or gem in setting or mounting](https://commons.wikimedia.org/wiki/Special:FilePath/Ring parts.svg?width=200 "bezel]], and 4) stone or gem in setting or mounting")
CIRCULAR BAND WORN AS A TYPE OF ORNAMENTAL JEWELLERY AROUND THE FINGER
Jewelry ring; Dinner ring; Finger ring; Bague; Finger-ring; Cocktail ring; Piece of jewelry ring; Ring (finger); Finger rings; 💍; Ring (jewelry); Penannular ring
·noun The annular molding or group of moldings dividing a long shaft or clustered column into two or more parts.
Ring (mathematics)
![[[Richard Dedekind]], one of the founders of [[ring theory]].](https://commons.wikimedia.org/wiki/Special:FilePath/Dedekind.jpeg?width=200 "[[Richard Dedekind]], one of the founders of [[ring theory]].")
![The [[integer]]s, along with the two operations of [[addition]] and [[multiplication]], form the prototypical example of a ring.](https://commons.wikimedia.org/wiki/Special:FilePath/Number-line.svg?width=200 "The [[integer]]s, along with the two operations of [[addition]] and [[multiplication]], form the prototypical example of a ring.")
ALGEBRAIC STRUCTURE IN MATHEMATICS, NOT NECESSARILY WITH MULTIPLICATIVE IDENTITY
Ring (algebra); Associative rings; Unit ring; Ring with a unit; Unital ring; Associative ring; Unitary ring; Ring (abstract algebra); Ring with unity; Ring with identity; Ring unit; Ring (math); Ring (maths); Ring mathematics; Ring maths; Ring math; Mathematical ring; Algebraic ring; Arithmetic properties; Ring with Unity; Unitary algebra; Ring axioms; Ring object; Ring of functions
In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. In other words, a ring is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers.
Examples of use of G-ring
1. Matt Hedman, an imaging team associate at Cornell University, Ithaca, N.Y. said, "I think our Cassini images of the D ring are providing new information about the dynamics and lifetimes of ring particles in a new regime, very close to the planet." The delicate G ring encircles the planet at about 170,000 kilometers (106,000 miles) from Saturn‘s center.