Quasi-excellence and formal series. (English) Zbl 0534.13011
The regularity of the morphism from A to A[[x]] is equivalent to the quasi-excellence of the noetherian local ring A. The proof uses on the one hand the homology theory of commutative algebras and on the other hand Rotthaus’ result on the completion of quasi-excellent rings.
MSC:
| 13E05 | Commutative Noetherian rings and modules |
| 13F25 | Formal power series rings |
| 13H05 | Regular local rings |
References:
| [1] | M. André - Localisation de la lissité formelle Manuscripta Mathematica 13(1974) 297-307 · Zbl 0287.18019 · doi:10.1007/BF01168230 |
| [2] | M. André - Homologie des algèbres commutatives Berlin - Springer Verlag 1974 |
| [3] | A. Brezuleanu - N. Radu - Lectii de Algebr? III Bucuresti - Mimeographed 1982 |
| [4] | Ch. Rotthaus - Komplettierung semi-lokaler quasiausgezeichneter Ringe. Nagoya Mathmatical Journal 76(1979) 173-180 |
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