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Rotthaus, Christel

Excellent rings, Henselian rings and the approximation property. (English) Zbl 0881.13009

Rocky Mt. J. Math. 27, No. 1, 317-334 (1997).
The author gives an overview on excellent rings, Henselian rings and the property of approximation. As an application she describes a solution of the Bass-Quillen conjecture obtained by Popescu and Spivakovsky. After M. Artin’s approximation theorem, the central result in the theory of excellent Henselian rings was proved by D. Popescu [Nagoya Math. J. 100, 97-126 (1985; Zbl 0561.14008) and 104, 85-115 (1986; Zbl 0592.14014)]:
An excellent Henselian ring has the property of (Artin) approximation.
This is a consequence of Popescu’s more general result:
A morphism between two Noetherian rings is regular if and only if it is a filtered inductive limit of smooth finite type morphisms.
At least after M. Spivakovsky’s paper [“Smoothing of ring homomorphisms, approximation theorems and the Bass-Quillen conjecture” (preprint 1993)] Popescu’s result and the validity of his proof was established in the mathematical community.
It seems that the author completely ignores this fact and knows only her own proof for a special case which appeared 1987. From this point of view the paper suggests a wrong picture.
Reviewer: G.Pfister (Kaiserslautern)

Cited in 9 Documents

MSC:

13F40 Excellent rings
13J15 Henselian rings
14B12 Local deformation theory, Artin approximation, etc.
13J10 Complete rings, completion

Keywords:

excellent rings; Henselian rings; approximation

Citations:

Zbl 0575.14010; Zbl 0598.14012; Zbl 0561.14008; Zbl 0592.14014
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\textit{C. Rotthaus}, Rocky Mt. J. Math. 27, No. 1, 317--334 (1997; Zbl 0881.13009)
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