Approximation property (ring theory)

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. The notion of the approximation property is due to Michael Artin.

This article is about the concept in ring theory. For the concept in functional analysis, see approximation property.
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