Abstract
In this paper, we prove the following theorem: “Let A be a complete Zariski ring with respect to the ideal
. If, for any maximal ideal
of A,
is an Akizuki ring and
is a Nagata ring, then
is also a Nagata ring, for any maximal ideal
of A⌉.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Bibliography
BOURBAKI, N.: Algèbre commutative, Hermann, Paris
GROTHENDIECK, A.: Eléments de Géométrie Algébrique, I, Grund. der Math., b.166, Springer Verlag, 1971
GROTHENDIECK, A.: Eléments de Géométrie Algébrique, IV, Publ. Math 24, IHES, Presses Universitaires de France, Paris
LAFON, J. P.: Algèbre Commutative, Hermann, Paris, 1977
MAROT, J.: Sur les anneaux universellement japonais, Bull. S.M.F.,103, 103–111, 1975
MAROT, J.: Limite inductive plate de P-anneaux, Journal of Algebra,57 (2), 484–496, 1979
MATIJEVIC, J. R.: Maximal ideal transforms of noetherian rings, Proc. A.M.S.,54, 49–52, 1976
MATSUMURA, H.: Commutative Algebra, W.A. Benjamin Inc., New-York, 1970
MORI, Y.: Remarks on noetherian local domains of dim 2, Journ. Reine und ange. Math., b242, 215–220, 1970
NAGATA, M.: Local rings, Interscience publishers, New-York, 1962
NISHIMURA, J.: On ideal-adic completion of noetherian rings, Kyoto University, to appear
ZARISKI, O. and SAMUEL, P.: Commutative Algebra, 1–2, Van Nostrand Comp. Princeton, 1967
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Marot, J. About Nagata rings. Manuscripta Math 33, 27–35 (1980). https://doi.org/10.1007/BF01298335
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01298335