In mathematics, in the fields of commutative algebra and algebraic geometry, an excellent ring is a Noetherian commutative ring with many of the good properties of complete local rings. This class of rings was defined by Alexander Grothendieck (1965).
Most Noetherian rings that occur in algebraic geometry or number theory are excellent, and excellence of a ring is closely related to resolution of singularities of the associated scheme (Hironaka (1964)).
Read more about Excellent Ring: Definitions, Examples, Resolution of Singularities
Famous quotes containing the words excellent and/or ring:
“Mrs. Sneed and her daughter, Miss Austine Sneed, are visiting us—Washington correspondents of excellent character.... We are much interested in their accounts of Washington affairs. Nothing could be further from our desire than to return to Washington and again enter its whirl, either socially or politically, but we are interested in seeing Washington with the roof off.”
—Rutherford Birchard Hayes (1822–1893)
“Interpreting the dance: young women in white dancing in a ring can only be virgins; old women in black dancing in a ring can only be witches; but middle-aged women in colors, square dancing...?”
—Mason Cooley (b. 1927)