- See also
- Notes
- References
{{about|the concept in ring theory|the concept in functional analysis|approximation property}}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.[[2] The notion of the approximation property is due to Michael Artin.] See also - Artin approximation theorem
- Popescu's theorem
Notes 1. ^1 {{Cite web|url=https://stacks.math.columbia.edu/tag/07BW|title=Tag 07BW: Smoothing Ring Maps|last=|first=|date=|website=The Stacks Project|publisher=Columbia University, Department of Mathematics|access-date=2018-02-19}}
[1]
}}References- {{cite journal|last=Popescu |first=Dorin |title=General Néron desingularization and approximation |journal=Nagoya Mathematical Journal |year=1986 |volume=104 |pages=85–115 |doi=10.1017/S0027763000022698 |url=https://projecteuclid.org/download/pdf_1/euclid.nmj/1118780554}}
- {{cite journal |last=Rotthaus |first=Christel |author-link=Christel Rotthaus |title=On the approximation property of excellent rings |journal=Inventiones mathematicae |year=1987 |volume=88 |pages=39–63 |doi=10.1007/BF01405090 }}
- {{cite journal |doi=10.1007/BF02684596 |title=Algebraic approximation of structures over complete local rings|journal=Publications Mathématiques de l'IHÉS|volume=36|pages=23–58|year=1969|last1=Artin|first1=M|issn=0073-8301}}
- {{cite journal |doi=10.1007/BF01389777 |title=On the solutions of analytic equations|journal=Inventiones Mathematicae|volume=5|issue=4|pages=277–291|year=1968|last1=Artin|first1=M|issn=0020-9910}}
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