A Homological Bridge between Finite and Infinite-Dimensional Representations of Algebras

Algebras and Representation Theory

Volumn 1, Issue 2, 1998, Pages 169-188

  Huisgen Zimmermann, B ^a   Smalo S O ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

Author keywords

Contravariant finiteness; Finistic dimensions; Modules of finite homological dimensions

Indexed keywords

EID: 0001910002     PISSN: 1386923X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1009948721602     Document Type: Article

References (22)

1. Auslander, M.: Representation theory of Artin algebras, II, Comm. Algebra 2 (1974), 269-310.
2. Auslander, M.: Large modules over Artin algebras, In: Algebra, Topology and Categories, Academic Press, New York, 1976.
3. Auslander, M. and Reiten, I.: Applications of contravariantly finite subcategories, Adv. in Math. 86(1991), 111-152.
4. Auslander, M. and Smalø, S. O.: Preprojective modules over Artin algebras, J. Algebra 66 (1980), 61-122.
5. Burgess, W. D. and Huisgen-Zimmermann, B.: Approximating modules by modules of finite projective dimension, J. Algebra 178 (1995), 48-91.
6. Crawley-Boevey, W.: Tame algebras and generic modules, Proc. London Math. Soc. 63 (1991), 241-265.
7. Crawley-Boevey, W.: Modules of finite length over their endomorphism rings, In: H. Tachikawa and S. Brenner (eds), Representations of Algebras and Related Topics, London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, Cambridge, 1992, pp. 127-184.
8. Crawley-Boevey, W.: Locally finitely presented additive categories, Comm. Algebra 22 (1994), 1641-1674.
9. (i), In: P. Dubreil and M.-P. Malliavin (eds), Sém. d'algèbre, Lecture Notes in Math. 867, Springer-Verlag, Berlin, 1981, pp. 234-294.
10. Happel, D. and Huisgen-Zimmermann, B.: Viewing finite-dimensional representations through infinite-dimensional ones, Pacific J. Math, (to appear).
11. Happel, D. and Unger, L.: Partial tilting modules and covariantly finite subcategories, Comm. Algebra 22 (1994), 1723-1727.
12. Huisgen-Zimmermann, B.: Predicting syzygies over monomial relation algebras, Manuscripta Math. 70 (1991), 157-182.
13. Huisgen-Zimmermann, B.: Homological domino effects and the first finitistic dimension conjecture, Invent. Math. 108 (1992), 369-383.
14. Huisgen-Zimmermann, B. and Smalø, S. O.: Covariant finiteness versus contravariant finiteness of categories of representations, In: S. K. Jain and S. T. Rizvi (eds), Advances in Ring Theory, Birkhäuser, Boston, 1997, pp. 129-144.
15. Igusa, K., Smalø, S. O. and Todorov, G.: Finite projectivity and contravariant finiteness, Proc. Amer. Math. Soc. 109 (1990), 937-941.
16. Kaplansky, I.: Projective modules, Ann. of Math. 68 (1958), 372-377.
17. Lenzing, H.: Homological transfer from finitely presented to infinite modules, In: Abelian Group Theory, Proc. Honolulu 1982/83, Lecture Notes in Math. 1006, Springer-Verlag, Berlin, 1983, pp. 734-761.
18. Raynaud, J. and Gruson, L.: Critères de platitude et de projectivité. Techniques de 'platification' d'un module, Invent. Math. 13 (1971), 1-89.
19. Ringel, C. M.: Infinite-dimensional representations of finite dimensional hereditary algebras, Ist. Naz. Alta Mat., Symp. Math. 23 (1979), 321-412.
20. Ringel, C. M. and Tachikawa, H.: QF-3 rings, J. reine angew. Math. 272 (1975), 49-72.
21. Smalø, S. O.: The supremum of the difference between the big and little finitistic dimensions is infinite, Proc. Amer. Math. Soc. 126 (1998), 2619-2622.
22. Zimmermann, W.: Rein-injektive direkte Summen von Moduln, Comm. Algebra 5 (1977), 1083-1117.