Frontiers of Mathematics in China >

2013 , Vol. 8 >Issue 6: 1367 - 1376

DOI: https://doi.org/10.1007/s11464-013-0328-4

RESEARCH ARTICLE

Approximations and cotorsion pairs related to a tilting pair

  • Yihua LIAO 1,2 ,
  • Jianlong CHEN , 1
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  • 1. Department of Mathematics, Southeast University, Nanjing 210096, China
  • 2. College of Mathematics and Information Science, Guangxi University, Nanning 530004, China

Received date: 17 Aug 2011

Accepted date: 23 May 2013

Published date: 01 Dec 2013

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

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.

Key words： Selforthogonal module; contravariantly (covariantly) finite subcategory; cotorsion pair; tilting pair

Cite this article

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

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Anderson F D, Fuller K R. Rings and Categories of Modules. 2nd ed. Berlin, New York: Springer-Verlag, 1992

DOI

2
Araya T, Yoshino Y. Remark on a depth formula, a grade inequality, and a conjecture of Auslander. Comm Algebra, 1998, 26: 3793-3806

DOI

3
Auslander M, Reiten I. Applications of contravariantly finite subcategories. Adv Math, 1991, 86: 111-152

DOI

4
Auslander M, Smalø S O. Preprojective modules over artin algebras. J Algebra, 1980, 66: 61-122

DOI

5
Avramov L L, Buchweitz R O. Support varieties and cohomology over complete intersections. Invent Math, 2000, 142: 285-318

DOI

6
Bazzoni S. A characterization of n-cotilting and n-tilting modules. J Algebra, 2004, 273: 359-372

DOI

7
Enochs E E, Jenda O M G. Relative Homological Algebra. Berlin, New York: Walter de Gruyter, 2000

DOI

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

DOI

11
Miyashita Y. Tilting modules associated with a series of idempotent ideals. J Algebra, 2001, 238: 485-501

DOI

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

DOI

13
Sega L M. Vanishing of cohomology over Gorenstein rings of small codimension. Proc Amer Math Soc, 2002, 131: 2313-2323

DOI

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

DOI

15
Wei J Q, Xi C C. A characterization of the tilting pair. J Algebra, 2007, 317(1): 376-391

DOI

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