Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T10:08:45.808Z Has data issue: false hasContentIssue false

On the base field change of P-rings and P-2 rings

Published online by Cambridge University Press:  22 January 2016

Hiroshi Tanimoto*
Affiliation:
Department of Mathematics, Nagoya University, Nagoya 464, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

One finds the following example in [3, (34, B)]:

Let k be a field of characteristic p and be n-variables over k. Then if p > 0 and [k : kp] = ∞, is an n-dimensional regular local ring but not a Nagata ring. In particular it is not an excellent ring.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1983

References

[ 1 ] Brezuleanu, A. and Radu, N., Excellent rings and good separation of the module of differentials, Rev. Roumaine Math. Pures Appl., 23 (1978), 14551470.Google Scholar
[ 2 ] Grothendieek, A. and Dieudonné, J., Éléments de Géométrie Algébrique, Ch. IV,. Première Partie, Pubi. IHES, No. 24 (1965), No.32 (1967).Google Scholar
[ 3 ] Matsumura, H., Commutative Algebra, Benjamin, New York (1970).Google Scholar
[ 4 ] Nagata, M., Local Rings, Interscience, New York (1962).Google Scholar
[ 5 ] Valabrega, P., On the excellent property for power series rings over polynomial rings, J. Math. Kyoto Univ., 15 (1975), 387395.Google Scholar
[ 6 ] Valabrega, P., Formal fibers and openness of loci, ibid., 18 (1978), 199208.Google Scholar
[ 7 ] Radu, N., Sur les algebres dont le module des différentielles est plat, Rev. Roumaine Math. Pures Appl., 21 (1976), 933939.Google Scholar