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The existence of flat covers
Authors:
Richard Belshoff, Edgar E. Enochs and Jin Zhong Xu
Journal:
Proc. Amer. Math. Soc. 122 (1994), 985-991
MSC:
Primary 16D50; Secondary 13C11
MathSciNet review:
1209416
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Abstract: We show that over a right coherent ring all pure injective left modules have flat covers. Then using recent work of Auslander and Buchweitz we show that left modules of finite flat dimension over right coherent rings also have flat covers.
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754698 (85j:13016), http://dx.doi.org/10.1090/S0002-9939-1984-0754698-X
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984044 (89m:16038), http://dx.doi.org/10.1016/0022-4049(89)90025-X
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(39 #4212)
- [1]
- M. Auslander and R. Buchweitz, The homological theory of maximal Cohen-Macauley approximations, Mém. Soc. Math. France (N.S.) 38 (1989), 5-37. MR 1044344 (91h:13010)
- [2]
- E. Enochs, Injective and flat covers, envelopes and resolvents, Israel J. Math. 39 (1981), 189-209. MR 636889 (83a:16031)
- [3]
- -, Flat covers and flat cotorsion modules, Proc. Amer. Math. Soc. 92 (1984), 179-184. MR 754698 (85j:13016)
- [4]
- -, Covers by flat modules and submodules of flat modules, J. Pure Appl. Algebra 57 (1989), 33-38. MR 984044 (89m:16038)
- [5]
- -, Torsion free covering modules, Proc. Amer. Math. Soc. 14 (1963), 884-889. MR 0168617 (29:5877)
- [6]
- L. Gruson and C. U. Jensen, Dimensions cohomologiques reliées aux foncteurs
 , Lecture Notes in Math., vol. 867, Springer-Verlag, New York and Berlin, 1981, pp. 234-294. MR 633523 (83d:16026)
- [7]
- M. Raynaud and L. Gruson, Critères de platitudes et de projectivité, Invent. Math. 13 (1971), 1-89. MR 0308104 (46:7219)
- [8]
- R. B. Warfield, Purity and algebraic compactness for modules, Pacific J. Math. 28 (1969), 699-719. MR 0242885 (39:4212)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1994-1209416-4
PII:
S 0002-9939(1994)1209416-4
Keywords:
Module,
flat,
injective,
cover
Article copyright:
© Copyright 1994 American Mathematical Society
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