Abstract
For a Nagata ring A, the module of absolute differentials is flat if and only if the morphism from AP into A is flat with a socalled elementary fibre. For the proof strong modules and basic rings are defined and studied. A complete local ring is basic and produces strong modules in a natural way.
Similar content being viewed by others
References
ANDRÉ, M.: Homologie des algèbres commutatives. Berlin-Heidelberg-New York: Springer 1974
ANDRÉ, M.: Localisation de la lissité formelle. Manuscripta Math.13, 297–307 (1974)
ANDRÉ, M.: Morphismes pseudo-réguliers. Comm. Algebra15, 2129–2142 (1987)
AVRAMOV, L.: Homology of local flat extensions and complete intersection defects. Math.Ann.228, 27–38 (1977)
BOURBAKI, N.: Algèbre commutative, chapitre 3. Paris: Hermann 1967
BREZULEANU, A., RADU, N.: Excellent rings and good separation of the module of differentials. Rev. Roumaine Math. Pures Appl.23, 1455–1471 (1978)
JENSEN, C.: Les foncteurs dérivés de\(\mathop {\lim }\limits_ \leftarrow \) et leurs applications en théorie des modules. Berlin-Heidelberg-New York: Springer 1972
KUNZ, E.: Kähler differentials. Braunschweig-Wiesbaden: Vieweg und Sohn 1986
KUNZ, E.: Characterizations of regular local rings of characteristic p. Amer. J. Math.91, 772–784 (1969)
KUNZ, E.: On noetherian rings of characteristic p. Amer. J. Math.98, 999–1013 (1976)
MATSUMURA, H.: Commutative algebra. New York: Benjamin 1970
MATSUMURA, H.: Commutative ring theory. Cambridge: Cambridge University Press 1986
TABAA, M.: Sur les homomorphismes d'intersection complète. C.R. Acad. Sci. Paris298, 437–439 (1984)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
André, M. Modules des differentielles en caracteristique p.. Manuscripta Math 62, 477–502 (1988). https://doi.org/10.1007/BF01357723
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01357723