Book Review
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MathSciNet review:
1567069
Full text of review:
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Book Information:
Author:
D. G. Northcott
Title:
Finite free resolutions
Additional book information:
Cambridge Univ. Press, New York, xii + 271 pp., $29.50.
Maurice Auslander and David A. Buchsbaum, Homological dimension in local rings, Trans. Amer. Math. Soc. 85 (1957), 390–405. MR 86822, DOI 10.1090/S0002-9947-1957-0086822-7
Maurice Auslander and D. A. Buchsbaum, Unique factorization in regular local rings, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 733–734. MR 103906, DOI 10.1073/pnas.45.5.733
S. Floyd Barger, A theory of grade for commutative rings, Proc. Amer. Math. Soc. 36 (1972), 365–368. MR 308106, DOI 10.1090/S0002-9939-1972-0308106-5
David A. Buchsbaum and David Eisenbud, What makes a complex exact?, J. Algebra 25 (1973), 259–268. MR 314819, DOI 10.1016/0021-8693(73)90044-6
David A. Buchsbaum and David Eisenbud, Some structure theorems for finite free resolutions, Advances in Math. 12 (1974), 84–139. MR 340240, DOI 10.1016/S0001-8708(74)80019-8
J. A. Eagon and D. G. Northcott, On the Buchsbaum-Eisenbud theory of finite free resolutions, J. Reine Angew. Math. 262(263) (1973), 205–219. MR 332759, DOI 10.1515/crll.1973.262-263.205
David Hilbert, Ueber die Theorie der algebraischen Formen, Math. Ann. 36 (1890), no. 4, 473–534 (German). MR 1510634, DOI 10.1007/BF01208503
M. Hochster, Grade-sensitive modules and perfect modules, Proc. London Math. Soc. (3) 29 (1974), 55–76. MR 374118, DOI 10.1112/plms/s3-29.1.55
Melvin Hochster, Topics in the homological theory of modules over commutative rings, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 24, Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, Providence, R.I., 1975. Expository lectures from the CBMS Regional Conference held at the University of Nebraska, Lincoln, Neb., June 24–28, 1974. MR 0371879
Irving Kaplansky, Projective modules, Ann. of Math (2) 68 (1958), 372–377. MR 0100017, DOI 10.2307/1970252
R. E. MacRae, On an application of the Fitting invariants, J. Algebra 2 (1965), 153–169. MR 178038, DOI 10.1016/0021-8693(65)90016-5
12. C. Peskine and L. Szpiro, Dimension projective finie et cohomologie locale, Publ. Math. Inst Haute Étude Sci; Paris, no. 42, 1973, 323-395.
Daniel Quillen, Projective modules over polynomial rings, Invent. Math. 36 (1976), 167–171. MR 427303, DOI 10.1007/BF01390008
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
- 1.
- M. Auslander and D. A. Buchsbaum, Homological dimension in local rings, Trans. Amer. Math. Soc. 85 (1957), 390-405. MR 0086822
- 2.
- M. Auslander and D. A. Buchsbaum, Unique factorization in regular local rings, Proc. Nat Acad. Sci. 45 (1959), 733-734. MR 103906
- 3.
- S. F. Barger, Generic perfection and the theory of grade, Thesis, University of Minnesota, 1970; also Proc. Amer. Math. Soc. 36 (1972), 365-368. MR 308106
- 4.
- D. A. Buchsbaum and D. Eisenbud, What makes a complex exact?, J. Algebra 25 (1973), 259-268. MR 314819
- 5.
- D. A. Buchsbaum and D. Eisenbud, Some structure theorems for finite free resolutions, Advances in Math. 12 (1974), 84-139. MR 340240
- 6.
- J. A. Eagon and D. G. Northcott, On the Buchsbaum-Eisenbud theory of finite free resolutions, J. Reine Angew. Math. 262/263 (1973), 205-219. MR 332759
- 7.
- D. Hilbert, Über die Theorie der algebraischen Formen, Math. Ann. 36 (1890), 473-534. MR 1510634
- 8.
- M. Hochster, Grade-sensitive modules and perfect modules, Proc. London Math. Soc. (3) 29 (1974), 55-76. MR 374118
- 9.
- M. Hochster, Topics in the homological theory of modules over commutative rings, CBMS Regional Conf. Ser. in Math., no. 24, Amer. Math. Soc., Providence, R.I., 1975, pp. 1-75. MR 371879
- 10.
- I. Kaplansky, Projective modules, Ann. of Math. (2) 68 (1958), 372-377. MR 100017
- 11.
- R. E. MacCrae, On an application of Fitting invariants, J. Algebra 2 (1965), 153-169. MR 178038
- 12.
- C. Peskine and L. Szpiro, Dimension projective finie et cohomologie locale, Publ. Math. Inst Haute Étude Sci; Paris, no. 42, 1973, 323-395.
- 13.
- D. Quillen, Projective modules over polynomial rings, Invent. Math. 36 (1976), 167-171. MR 427303
- 14.
- J.-P. Serre, Sur la dimension homologique des anneaux et des modules noethériens, Proc. Internat. Sympos. on Algebraic Number Theory, Tokyo, 1955, pp. 175-189. MR 86071
Review Information:
Reviewer:
M. Hochster
Journal:
Bull. Amer. Math. Soc.
84 (1978), 652-656
DOI:
https://doi.org/10.1090/S0002-9904-1978-14514-5