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A note on universally catenary rings

Published online by Cambridge University Press:  22 January 2016

Silvio Greco*
Affiliation:
Instituto Matematico Politecnico, Torino, Italy and Department of Mathematics, Nagoya University, Nagoya, Japan
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The following two related problems in Commutative Algebra are certainly very popular:

  1. 1. Study the permanence of properties from a ring A to an idealadic completion of A; and

  2. 2. Study the lifting of properties from A/I to A where A is a ring which is complete and separated in the I-adic topology.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

[1] Greco, S., Two theorems on excellent rings, Nagoya Math. J., 60 (1976), 139159.CrossRefGoogle Scholar
[2] Greco, S. and Salmon, P., Topics in m-adic topologies, Erg. der Math. b. 58, Springer Verlag, 1971.Google Scholar
[3] Grothendieck, A., Eléments de Géométrie Algébrique, ch. IV, part 2, Publ. Math. n. 24, IHES, Paris 1964.Google Scholar
[4] Grothendieck, A., Eléments de Géométrie Algébrique, ch. IV, part 3, Publ. Math n. 28, IHES, Paris 1965.Google Scholar
[5] Kaplanski, I., Commutative rings, revised edition, The University of Chicago Press, Chicago 1974.Google Scholar
[6] Matsumura, H., Commutative Algebra, second edition, Benjamin/Cummings Publishing Company, 1980.Google Scholar
[7] Nagata, M., Local rings, Interscience, 1962.Google Scholar
[8] Pedrini, C., Incollamenti e gruppi di Picard, Rend. Sem. Mat. Univ. Padova, 48 (1972), 3966.Google Scholar
[9] Ratliff, L. J. Jr., On quasi-unmixed local domains, the altitude formula, and the chain condition for prime ideals (II), Amer. J. Math., 92 (1970), 99144.Google Scholar
[10] Rotthaus, C., Komplettierung semilocaler quasiausgezeichnete ringe, Nagoya Math. J., 76 (1979), 173180.Google Scholar
[11] Seydi, H., Anneaux henseliens et conditions de chaines, Bull. Soc. Math. France, 99 (1970), 931.CrossRefGoogle Scholar
[12] Seydi, H., Sur la theorie des anneaux excellents en characteristique p, II, J. Math. Kyoto Univ., 20 (1980), 155197.Google Scholar
[13] Zariski, O. and Samuel, P., Commutative Algebra, vol. II, Van Nostrand 1960.Google Scholar