Gorenstein flat covers of modules over gorenstein rings

Journal of Algebra

Volumn 181, Issue 1, 1996, Pages 288-313

  Enochs, Edgar ^a   Xu, Jinzhong ^a  

^a UNIVERSITY OF KENTUCKY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030119983     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1006/jabr.1996.0121     Document Type: Article

References (23)

1. 1. M. Auslander, "Anneaux de Gorenstein et torsion en algèbre commutative," Séminaire d'algèbre, Ecole Normal Supérieure de Jeunes Filles, Paris, 1966/67.
2. 2. M. Auslander and R. Buchweitz, The homological theory of maximal Cohen-Macaulay approximations, Soc. Math. France Mem. 38 (1989), 15-37.
3. 3. M. Auslander and I. Reiten, Applications of contravariantly finite subcategories, Adv. Math. 86 (1991), 111-152.
4. 4. H. Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466-488.
5. 5. S. Ding, Cohen-Macaulay approximation and multiplicity, J. Algebra 153 (1992), 271-288.
6. 6. S. Ding, The associated graded ring and the index of a gorenstein local ring, Proc. Amer. Math. Soc. 120, No. 4 (1994), 129-133.
7. 7. B. Eckmann and A. Schopf, Ueber injective moduln, Arch. Math. 4, No. 2 (1953), 75-78.
8. 8. O. Jenda, E. Enochs, and B. Torrecillas, Gorenstein flat modules, J. Nanjing Univ. 10 (1993), 1-9.
9. 9. E. Enochs, Injective and flat covers, envelopes and resolvents, Israel J. Math. 39 (1981), 189-209.
10. 10. L. Fuchs, Algebraically compact modules over noetherian rings, Indian J. Math. 9, No. 2 (1967), 357-374.
11. 11. Y. Iwanaga, On rings with finite self-injective dimension, Comm. Algebra 7, No. 4 (1979), 393-414.
12. 12. Y. Iwanaga, On rings with finite self-injective dimension II, Tsukuba J. Math. 4 (1980), 107-113.
13. ← et leurs Applications en Théorie des Modules," Lectures on Injective Modules and Quotients Rings, Vol. 254, Springer-Verlag, Berlin/New York, 1972.
14. 14. J. Asensio Mayor and J. Martinez Hernandez, Flat envelopes in commutative rings, Israel J. Math. 62, No. 1 (1988), 123-128.
15. 15. J. Asensio Mayor and J. Martinez Hernandez, Monomorphic flat envelopes in commutative rings, Arch. Math. (Basel) 54, No. 5 (1990), 430-435.
16. 16. M. Raynaud and L. Gruson, Critères de platitude et de projectivité, Invent. Math. 13 (1971), 1-89.
17. 17. E. Enochs, R. Belshoff, and J. Xu, The existence of flat covers, Proc. Amer. Math. Soc. 122, No. 4 (1994), 985-991.
18. 18. P. Roberts, "Homological Invariants of Modules over Commutative Rings," Les Presses de I'Univ. de Montreal, 1980.
19. 19. S. Eilenberg and T. Nakayama, On the dimension of modules and algebras II, Nagoya Math. J. 9 (1953), 13-25.
20. 20. V. Akatsa, "Flat Envelopes and Negative Torsion Functors," Ph.D. thesis, University of Kentucky, 1991.
21. 21. R. B. Warfield, Purity and algebraic compactness for modules, Pacific J. Math. 28 (1969), 699-719.
22. 22. J. Xu, Minimal injective and flat resolutions of modules over Gorenstein rings, J. Algebra 175 (1995) 451-477.
23. 23. J. Xu, The existence of flat covers over noetherian ring of finite krull dimension, Proc. Amer. Math. Soc. 123, No. 1 (1995), 27-32.