Frontiers of Mathematics in China >
Approximations and cotorsion pairs related to a tilting pair
Received date: 17 Aug 2011
Accepted date: 23 May 2013
Published date: 01 Dec 2013
Copyright
The notion of a tilting pair over artin algebras was introduced by Miyashita in 2001. It is a useful tool in the tilting theory. Approximations and cotorsion pairs related to a fixed tilting pair were discussed. A contravariantly (covariantly) finite subcategory and a cotorsion pair associated with a fixed tilting pair were given in this paper.
Yihua LIAO , Jianlong CHEN . Approximations and cotorsion pairs related to a tilting pair[J]. Frontiers of Mathematics in China, 2013 , 8(6) : 1367 -1376 . DOI: 10.1007/s11464-013-0328-4
1 |
Anderson F D, Fuller K R. Rings and Categories of Modules. 2nd ed. Berlin, New York: Springer-Verlag, 1992
|
2 |
Araya T, Yoshino Y. Remark on a depth formula, a grade inequality, and a conjecture of Auslander. Comm Algebra, 1998, 26: 3793-3806
|
3 |
Auslander M, Reiten I. Applications of contravariantly finite subcategories. Adv Math, 1991, 86: 111-152
|
4 |
Auslander M, Smalø S O. Preprojective modules over artin algebras. J Algebra, 1980, 66: 61-122
|
5 |
Avramov L L, Buchweitz R O. Support varieties and cohomology over complete intersections. Invent Math, 2000, 142: 285-318
|
6 |
Bazzoni S. A characterization of n-cotilting and n-tilting modules. J Algebra, 2004, 273: 359-372
|
7 |
Enochs E E, Jenda O M G. Relative Homological Algebra. Berlin, New York: Walter de Gruyter, 2000
|
8 |
Enochs E E, Oyonarte L. Covers, Envolopes, and Cotorsion Theories. New York: Nova Science Publishers, Inc, 2002
|
9 |
Garcia R J R. Covers and Envelopes in the Category of Complexes of Modules. London: Chapman & Hall/CRC, 1999
|
10 |
Göbel R, Trlifaj J. Approximations and Endomorphism Algebras of Modules. Berlin, New York: Walter de Gruyter, 2006
|
11 |
Miyashita Y. Tilting modules associated with a series of idempotent ideals. J Algebra, 2001, 238: 485-501
|
12 |
Reiten I. Tilting theory and homologically finite subcategories with applications to quasihereditary algebras. In: Handbook of Tilting Theory. London Math Soc Lect Note Ser, 332. Cambridge: Cambridge Univ Press, 2007, 179-214
|
13 |
Sega L M. Vanishing of cohomology over Gorenstein rings of small codimension. Proc Amer Math Soc, 2002, 131: 2313-2323
|
14 |
Trlifaj J. Infinite dimensional tilting modules and cotorsion pairs. In: Handbook of Tilting Theory. London Math Soc Lect Note Ser, 332. Cambridge: Cambridge Univ Press, 2007: 279-322
|
15 |
Wei J Q, Xi C C. A characterization of the tilting pair. J Algebra, 2007, 317(1): 376-391
|
/
〈 | 〉 |