In algebra, a commutative Noetherian ring A is said to have the approximation property with respect to an ideal I if each finite system of polynomial equations with coefficients in A has a solution in A if and only if it has a solution in the I-adic completion of A.[1][2] The notion of the approximation property is due to Michael Artin.

See also

Notes

  1. Rotthaus, Christel (1997). "Excellent Rings, Henselian Rings, and the Approximation Property". Rocky Mountain Journal of Mathematics. 27 (1): 317–334. doi:10.1216/rmjm/1181071964. JSTOR 44238106.
  2. "Tag 07BW: Smoothing Ring Maps". The Stacks Project. Columbia University, Department of Mathematics. Retrieved 2018-02-19.

References


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