Homological dimension and the continuum hypothesis
HTML articles powered by AMS MathViewer
- by B. L. Osofsky
- Trans. Amer. Math. Soc. 132 (1968), 217-230
- DOI: https://doi.org/10.1090/S0002-9947-1968-0224606-4
- PDF | Request permission
References
- Maurice Auslander, On the dimension of modules and algebras. III. Global dimension, Nagoya Math. J. 9 (1955), 67–77. MR 74406
- Maurice Auslander and David A. Buchsbaum, Homological dimension in noetherian rings. II, Trans. Amer. Math. Soc. 88 (1958), 194–206. MR 96720, DOI 10.1090/S0002-9947-1958-0096720-1
- Hyman Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466–488. MR 157984, DOI 10.1090/S0002-9947-1960-0157984-8
- Hyman Bass, Big projective modules are free, Illinois J. Math. 7 (1963), 24–31. MR 143789
- Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480
- Paul J. Cohen, Set theory and the continuum hypothesis, W. A. Benjamin, Inc., New York-Amsterdam, 1966. MR 0232676
- Irving Kaplansky, Projective modules, Ann. of Math. (2) 68 (1958), 372–377. MR 0100017, DOI 10.2307/1970252 —, Homological dimension of rings and modules, Mimeographed notes, Univ. of Chicago, Illinois, 1959.
- Irving Kaplansky, The homological dimension of a quotient field, Nagoya Math. J. 27 (1966), 139–142. MR 194454
- Eben Matlis, Divisible modules, Proc. Amer. Math. Soc. 11 (1960), 385–391. MR 116044, DOI 10.1090/S0002-9939-1960-0116044-8
- Eben Matlis, Cotorsion modules, Mem. Amer. Math. Soc. 49 (1964), 66. MR 178025
- 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
- B. L. Osofsky, Global dimension of valuation rings, Trans. Amer. Math. Soc. 127 (1967), 136–149. MR 206074, DOI 10.1090/S0002-9947-1967-0206074-0 L. Small, Some remarks on the homological dimension of a quotient field, Mimeographed notes, Univ. of California, Berkeley, Calif., 1966.
- Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0120249
Bibliographic Information
- © Copyright 1968 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 132 (1968), 217-230
- MSC: Primary 13.90; Secondary 18.00
- DOI: https://doi.org/10.1090/S0002-9947-1968-0224606-4
- MathSciNet review: 0224606