Book Review
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MathSciNet review:
1567538
Full text of review:
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Book Information:
Author:
N. Bourbaki
Title:
Éléments de mathématique. Algèbre commutative
Additional book information:
Chapitres 8 et 9, Masson, Paris, 1983, 200 pp., 150F. ISBN 2-2257-8716-6.
1. W. Krull, Dimensionstheorie in Stellenringen, J. Reine Angew. Math. 179 (1938), 204-226.
Claude Chevalley, On the theory of local rings, Ann. of Math. (2) 44 (1943), 690–708. MR 9603, DOI 10.2307/1969105
Claude Chevalley, Intersections of algebraic and algebroid varieties, Trans. Amer. Math. Soc. 57 (1945), 1–85. MR 12458, DOI 10.1090/S0002-9947-1945-0012458-1
I. S. Cohen, On the structure and ideal theory of complete local rings, Trans. Amer. Math. Soc. 59 (1946), 54–106. MR 16094, DOI 10.1090/S0002-9947-1946-0016094-3
Pierre Samuel, La notion de multiplicité en algèbre et en géométrie algébrique, J. Math. Pures Appl. (9) 30 (1951), 159–205 (French). MR 48103
Jean-Pierre Serre, Sur la dimension homologique des anneaux et des modules noethériens, Proceedings of the international symposium on algebraic number theory, Tokyo & Nikko, 1955, Science Council of Japan, Tokyo, 1956, pp. 175–189 (French). MR 0086071
Masayoshi Nagata, The theory of multiplicity in general local rings, Proceedings of the international symposium on algebraic number theory, Tokyo & Nikko, 1955, Science Council of Japan, Tokyo, 1956, pp. 191–226. MR 0082966
Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0155856
- 1.
- W. Krull, Dimensionstheorie in Stellenringen, J. Reine Angew. Math. 179 (1938), 204-226.
- 2.
- C. Chevalley, On the theory of local rings, Ann. of Math. (2) 44 (1943), 690-708. MR 0009603
- 3.
- C. Chevalley, Intersections of algebraic and algebroid varieties, Trans. Amer. Math. Soc. 57 (1945), 1-85. MR 12458
- 4.
- I. S. Cohen, On the structure and ideal theory of complete local rings, Trans. Amer. Math. Soc. 59 (1946), 54-106. MR 16094
- 5.
- M. Samuel, La notion de multiplicité en algèbre et en géométrie algébrique, J. Math. Pures Appl. 30 (1951), 159-274; These, Paris, 1951. MR 48103
- 6.
- J.-P. Serre, Sur la dimension homologique des anneaux et des modules noetherian, Proc. Internat. Sympos. (Tokyo-Nikko, 1955), Scientific Council of Japan, Tokyo, 1956, pp. 175-189. MR 86071
- 7.
- M. Nagata, The theory of multiplicity in general local rings, Proc. Internat. Sympos. (Tokyo-Nikko, 1955), Scientific Council of Japan, Tokyo, 1956, pp. 191-226. MR 82966
- 8.
- M. Nagata, Local rings, Wiley, New York, 1962; reprint, Kreager, Huntington. MR 155856
Review Information:
Reviewer:
M. Nagata
Journal:
Bull. Amer. Math. Soc.
12 (1985), 175-177
DOI:
https://doi.org/10.1090/S0273-0979-1985-15338-8