Excellent rings, Henselian rings and the approximation property
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 \textit{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 \textit{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.
scientific article; zbMATH DE number 1051538
scientific article