Tilting preenvelopes and cotilting precovers

Algebras and Representation Theory

Volumn 4, Issue 2, 2001, Pages 155-170

  Hügel, Lidia Angeleri ^a   Tonolo, Alberto ^b   Trlifaj, Jan ^c  

^a UNIVERSITY OF MUNICH   (Germany)

^b UNIVERSITY OF PADOVA   (Italy)

^c CHARLES UNIVERSITY   (Czech Republic)

Author keywords

Cofinendo; Cotilting modules; Finendo; Precovers; Preenvelopes; Tilting modules

Indexed keywords

EID: 0342467833     PISSN: 1386923X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1011485800557     Document Type: Article

References (22)

1. Assem, I.: Torsion theories induced by tilting modules, Canad. J. Math. 36 (1984), 899-913.
2. Auslander, M. and Reiten, I.: Applications of contravariantly finite subcategories, Adv. Math. 86 (1991), 111-152.
3. Auslander, M. and Smalø, S. O.: Preprojective modules over Artin algebras, J. Algebra 66 (1980), 61-122.
4. Brenner, S. and Butler, M.: Generalizations of the Bernstein-Gelfand-Ponomarev reflection functors, In: Proc. ICRA II, Lecture Notes in Math. 832, Springer, New York, 1980, pp. 103-169.
5. Cartan, H. and Eilenberg, S.: Homological Algebra, Princeton Univ. Press, Princeton, 1956.
6. Colby, R. R. and Fuller, K. R.: Tilting, cotilting and serially tilted rings, Comm. Algebra 18 (1990), 1585-1615.
7. Colpi, R., D'Este, G. and Tonolo, A.: Quasi-tilting modules and counter equivalences, J. Algebra 191 (1997), 461-494.
8. Colpi, R. and Menini, C.: On the structure of *-modules, J. Algebra 158 (1993), 400-419.
9. Colpi, R., Tonolo, A. and Trlifaj, J.: Partial cotilting modules and the lattices induced by them, Comm. Algebra 25 (1997), 3225-3237.
10. Colpi, R. and Trlifaj, J.: Tilting modules and tilting torsion theories, J. Algebra 178 (1995), 614-634.
11. Enochs, E.: Injective and flat covers, envelopes and resolvents, Israel J. Math 39 (1981), 189-209.
12. Fuchs, L.: Infinite Abelian Groups, Vol. I, Academic Press, New York, 1970.
13. Fuchs, L. and Salce, L.: Modules over Valuation Domains, Marcel Dekker, New York, 1985.
14. Göbel, R. and Trlifaj, J.: Cotilting and a hierarchy of almost cotorsion groups, J. Algebra 224 (2000), 110-122.
15. Golan, J. S. and Teply, M. L.: Torsion-free covers, Israel J. Math 15 (1973), 237-256.
16. Happel, D. and Ringel, C. M.: Tilted algebras, Trans. Amer. Math. Soc. 274 (1982), 399-443.
17. Miyashita, Y.: Tilting modules of finite projective dimension, Math. Z. 193 (1986), 113-146.
18. Rada, J. and Saorin, M.: Rings characterized by (pre)envelopes and (pre)covers of their modules, Comm. Algebra 26 (1998), 899-912.
19. Smalø, S.: Torsion theories and tilting modules, Bull. London Math. Soc. 16 (1984), 518-522.
20. Teply, M. L.: Torsion-free covers II, Israel J. Math 23 (1976), 132-136.
21. Trlifaj, J.: Whitehead test modules, Trans. Amer. Math. Soc. 348 (1996), 1521-1554.
22. Xu, J.: Flat Covers of Modules, Lecture Notes in Math. 1634, Springer, New York, 1996.