|
Cotilting modules are pure-injective
Author(s):
S.
Bazzoni
Journal:
Proc. Amer. Math. Soc.
131
(2003),
3665-3672.
MSC (1991):
Primary 16D90, 16D30
Posted:
February 28, 2003
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We prove that a cotilting module over an arbitrary ring is pure-injective.
References:
-
- 1.
- L. Angeleri Hügel, A. Tonolo, J. Trlifaj, Tilting preenvelopes and cotilting precovers, Algebr. Represent. Theory 4 (2001), 155-170. MR 2002e:16010
- 2.
- M. Auslander, I. Reiten, Applications of contravariantly finite subcategories, Adv. Math. 86 (1991), 111-152. MR 92e:16009
- 3.
- M. Auslander, S. Smalø, Preprojective modules over Artin algebras, J. Algebra 66 (1980), 61-122. MR 83a:16039
- 4.
- L. Bican, R. El Bashir and E. Enochs, All modules have flat covers, Bull. London Math. Soc. 33, no. 4 (2001), 385-390. MR 2002e:16002
- 5.
- S. Brenner, M. Butler, Generalizations of the Bernstein-Gelfand-Ponomarev reflection functors, in Proc. ICRA III LNM 832, Springer (1980), 103-169. MR 83e:16031
- 6.
- A. B. Buan, H. Krause, Ø. Solberg, On the lattice of cotilting modules, AMA Algebra Montp. Announc., 1 (2002), 6pp.
- 7.
- R. R. Colby, K. R. Fuller, Tilting, cotilting and serially tilted rings, Comm. Algebra 18(5) (1990), 1585-1615. MR 91h:16011
- 8.
- R. Colpi, Tilting modules and *-modules, Comm. Algebra 21 (1993), 1095-1102. MR 94d:16009
- 9.
- R. Colpi, A. Tonolo, J. Trlifaj, Partial cotilting modules and the lattices induced by them, Comm. Algebra 25(10) (1997), 3225-3237. MR 98i:16003
- 10.
- R. Colpi, J. Trlifaj, Tilting modules and tilting torsion theories, J. Algebra 178 (1995), 492-510. MR 97e:16003
- 11.
- W. W. Crawley-Boevey, Infinite-dimensional modules in the representation theory of finite-dimensional algebras, Algebras and modules, I (Trondheim, 1996), 29-54. MR 99m:16016
- 12.
- P. C. Eklof and J. Trlifaj, How to make Ext vanish, Bull. London Math. Soc. 33 (2001), 41-51. MR 2001i:16015
- 13.
- P. C. Eklof, J. Trlifaj, Covers induced by Ext, J. Algebra 231 (2000), 640-651. MR 2001f:16021
- 14.
- E. Enochs, Injective and flat covers, envelopes and resolvents, Israel J. Math. 39 (1981), 33-38. MR 83a:16031
- 15.
- R. Göbel, S. Shelah, Almost free splitters, Colloq. Math. 81 (1999), no. 2, 193-221. MR 2000m:20092
- 16.
- R. Göbel, S. Shelah, Cotorsion theories and splitters, Trans. Amer. Math.Soc. 352 (2000), no. 11, 5357-5379. MR 2001b:20098
- 17.
- P. Griffith, On a subfunctor of Ext, Arch. Math. XXI (1970), 17-22. MR 41:6964
- 18.
- C. U. Jensen, H. Lenzing, Model Theoretic Algebra, Gordon and Breach S. Publishers, (1989). MR 91m:03038
- 19.
- D. Happel, C. Ringel, Tilted algebras, Trans. Amer. Math. Soc. 274 (1982), 399-443. MR 84d:16027
- 20.
- R. H. Hunter, Balanced subgroups of abelian groups, Trans. Amer. Math. Soc. 215 (1976), 81-98. MR 58:22337
- 21.
- H. Krause, Ø. Solberg, Filtering modules of finite projective dimension, to appear in Forum Math.
- 22.
- F. Mantese, P. Ruzicka, A. Tonolo, Cotilting versus pure-injective modules, to appear in Pacific J. Math.
- 23.
- Y. Miyashita, Tilting modules of finite projective dimension, Math. Z. 193 (1986), 113-146. MR 87m:16055
- 24.
- L. Salce, Cotorsion theories for abelian groups, Symposia Math., XXIII (1979), 11-32. MR 81j:20078
- 25.
- B. Stenström, Rings of quotients, GTM, 131, Springer-Verlag, New York (1975). MR 52:10782
- 26.
- J. Xu, Flat covers of modules, Lecture Notes in Mathematics No. 1634, Springer-Verlag, New York (1996). MR 98b:16003
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
16D90, 16D30
Retrieve articles in all Journals with MSC
(1991):
16D90, 16D30
Additional Information:
S.
Bazzoni
Affiliation:
Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Belzoni 7, 35131 Padova, Italy
Email:
bazzoni@math.unipd.it
DOI:
10.1090/S0002-9939-03-06938-7
PII:
S 0002-9939(03)06938-7
Keywords:
Cotilting modules,
pure-injective modules,
cotorsion theories
Received by editor(s):
May 31, 2002
Received by editor(s) in revised form:
July 10, 2002
Posted:
February 28, 2003
Additional Notes:
This research was supported by MURST
Communicated by:
Martin Lorenz
Copyright of article:
Copyright
2003,
American Mathematical Society
|
Comments: webmaster@ams.org