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

Notes

  1. ↑ Rotthaus, Christel (1997). "Excellent Rings, Henselian Rings, and the Approximation Property". Rocky Mountain Journal of Mathematics. 27: 317. 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

  • Popescu, Dorin (1986). "General Néron desingularization and approximation". Nagoya Mathematical Journal. 104: 85&ndash, 115. doi:10.1017/S0027763000022698.
  • Rotthaus, Christel (1987). "On the approximation property of excellent rings". Inventiones mathematicae. 88: 39&ndash, 63. doi:10.1007/BF01405090.
  • Artin, M (1969). "Algebraic approximation of structures over complete local rings". Publications mathématiques de l'IHÉS. 36: 23. doi:10.1007/BF02684596. ISSN 0073-8301.
  • Artin, M (1968). "On the solutions of analytic equations". Inventiones Mathematicae. 5 (4): 277. doi:10.1007/BF01389777. ISSN 0020-9910.


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