High Quality Content by WIKIPEDIA articles! 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)).

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