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.^[1][2] The notion of the approximation property is due to Michael Artin.

See also

• Artin approximation theorem
• Popescu's theorem