Rings for which certain flat modules are projective
HTML articles powered by AMS MathViewer
- by S. H. Cox and R. L. Pendleton
- Trans. Amer. Math. Soc. 150 (1970), 139-156
- DOI: https://doi.org/10.1090/S0002-9947-1970-0262296-4
- PDF | Request permission
References
- Maurice Auslander and David A. Buchsbaum, Invariant factors and two criteria for projectivity of modules, Trans. Amer. Math. Soc. 104 (1962), 516–522. MR 157987, DOI 10.1090/S0002-9947-1962-0157987-5
- 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
- N. Bourbaki, Éléments de mathématique. Première partie. Fascicule VI. Livre II: Algèbre. Chapitre 2: Algèbre linéaire, Actualités Sci. Indust., No. 1236, Hermann, Paris, 1962 (French). Troisième édition, entièrement refondue. MR 0155831 —, Livre II: Algèbre. Chapter 3; Algèbre multilinéaire, Actualités Sci. Indust., No. 1044, Hermann, Paris, 1958. MR 30 #3104. —, Algèbre commutative, Actualités Sci. Indust., Nos. 1290, 1293, 1308, Hermann, Paris, 1961-65. MR 30 #2027; MR 36 #146; MR 33 #2660.
- Stephen U. Chase, Direct products of modules, Trans. Amer. Math. Soc. 97 (1960), 457–473. MR 120260, DOI 10.1090/S0002-9947-1960-0120260-3
- S. H. Cox Jr., Determinantal rank and flat modules, Proc. Amer. Math. Soc. 22 (1969), 104–108. MR 241405, DOI 10.1090/S0002-9939-1969-0241405-4
- Shizuo Endo, On flat modules over commutative rings, J. Math. Soc. Japan 14 (1962), 284–291. MR 179226, DOI 10.2969/jmsj/01430284 A. Grothendieck, Éléments de géométrie algébrique. I: Le langage des schémas, Inst. Hautes Études Sci. Publ. Math. No. 4 (1960). MR 29 #1210.
- John G. Hocking and Gail S. Young, Topology, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1961. MR 0125557
- S. M. Kaye, Ring theoretic properties of matrix rings, Canad. Math. Bull. 10 (1967), 365–374. MR 213395, DOI 10.4153/CMB-1967-034-3
- Daniel Lazard, Disconnexités des spectres d’anneaux et des préschémas, Bull. Soc. Math. France 95 (1967), 95–108 (French). MR 223374 —, Algèbre symmétrique et platitude, C.R. Acad. Sci. Paris, Sér. A-B 264 (1967), A228-A230. MR 36 #152.
- Daniel Lazard, Sur les modules plats, C. R. Acad. Sci. Paris 258 (1964), 6313–6316 (French). MR 168625
- Lawrence S. Levy, Commutative rings whose homomorphic images are self-injective, Pacific J. Math. 18 (1966), 149–153. MR 194453
- K. R. Mount, Some remarks on Fitting’s invariants, Pacific J. Math. 13 (1963), 1353–1357. MR 162824
- 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, Upper bounds on homological dimensions, Nagoya Math. J. 32 (1968), 315–322. MR 232805
- R. S. Pierce, Modules over commutative regular rings, Memoirs of the American Mathematical Society, No. 70, American Mathematical Society, Providence, R.I., 1967. MR 0217056 F. L. Sandomierski and D. E. Smith, Rings for which finitely generated flat modules are projective, (to appear).
- Wolmer V. Vasconcelos, On finitely generated flat modules, Trans. Amer. Math. Soc. 138 (1969), 505–512. MR 238839, DOI 10.1090/S0002-9947-1969-0238839-5
- Wolmer V. Vasconcelos, On projective modules of finite rank, Proc. Amer. Math. Soc. 22 (1969), 430–433. MR 242807, DOI 10.1090/S0002-9939-1969-0242807-2
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 150 (1970), 139-156
- MSC: Primary 16.50
- DOI: https://doi.org/10.1090/S0002-9947-1970-0262296-4
- MathSciNet review: 0262296