On contravariant finiteness of subcategories

of modules of projective dimension

Author:
Bangming Deng

Journal:
Proc. Amer. Math. Soc. **124** (1996), 1673-1677

MSC (1991):
Primary 16P20, 18G20

DOI:
https://doi.org/10.1090/S0002-9939-96-03438-7

MathSciNet review:
1340382

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be an artin algebra. This paper presents a sufficient condition for the subcategory of to be contravariantly finite in , where is the subcategory of consisting of --modules of projective dimension less than or equal to . As an application of this condition it is shown that is contravariantly finite in for each when is stably equivalent to a hereditary algebra.

**1.**M. Auslander and I. Reiten,*Applications of contravariantly finite subcategories*, Adv. in Math.**86**(1991), 111--152. MR**92e:16009****2.**M. Auslander and S. O. Smalø,*Preprojective modules over artin algebras*, J. Algebra**66**(1980), 61--122. MR**83a:16039****3.**------,*Almost split sequences in subcategories*, J. Algebra**69**(1981), 426--454. MR**82j:16048a****4.**P. Gabriel, B. Keller, and A. V. Roiter,*Representations of finite--dimensional algebras*, Encyclopaedia of Math. Sci., vol. 73, Springer, Berlin, 1992. MR**94h:16001b****5.**K. Igusa, S. O. Smalø, and G. Todorov,*Finite projectivity and contravariant finiteness*, Proc. Amer. Math. Soc.**109**(1990), 937--941. MR**91b:16010****6.**S. O. Smalø,*Functorial finite subcategories over triangular matrix rings*, Proc. Amer. Math. Soc.**111**(1991), 651--656. MR**91f:16016**

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Additional Information

**Bangming Deng**

Affiliation:
Department of Mathematics, Beijing Normal University, Beijing 100875, People’s Republic of China

Email:
dengbm@bnu.ihep.ac.cn

DOI:
https://doi.org/10.1090/S0002-9939-96-03438-7

Received by editor(s):
November 30, 1994

Additional Notes:
Supported by the Postdoctoral Science Foundation of China.

Communicated by:
Ken Goodearl

Article copyright:
© Copyright 1996
American Mathematical Society