Artin approximation theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-02-18

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Artin_approximation_theorem


00:00:29 1 Statement of the theorem
00:00:36 2 Discussion
00:01:35 3 Alternative statement
00:02:07 4 See also
00:03:32 5 References



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SUMMARY
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In mathematics, the Artin approximation theorem is a fundamental result of Michael Artin (1969) in deformation theory which implies that formal power series with coefficients in a field k are well-approximated by the algebraic functions on k.
More precisely, Artin proved two such theorems: one, in 1968, on approximation of complex analytic solutions by formal solutions (in the case k = C); and an algebraic version of this theorem in 1969.