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Contravariantly Finite Subcategories and Torsion Theories

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Contravariantly finite subcategories have been useful in differentaspects of representation theory (Auslander and Reiten, 1989, 1991;Auslander and Smalø, 1981) and they appear very naturally, forexample, the torsion class of a torsion theory is contravariantly finite. Inthis paper we explore further relations between contravariantly finite,resolving, subcategories and torsion theories. We study these connections inthe category of functors that vanishes on projectives. Our resultsgeneralize some theorems we obtained previously in our interpretation ofNakayama’s conjecture (Martínez-Villa, 1994).

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References

  1. Auslander, M. and Reiten, I.: Representation theory of Artin algebras VI, Comm. Algebra 6 (1978), 257–300.

    Google Scholar 

  2. Auslander, M. and Reiten, I.: Stable equivalence of dualizing R-varieties I, Advances in Math. 12 (1974), 306–366.

    Google Scholar 

  3. Auslander, M. and Reiten, I.: Applications of Contravariantly Finite Subcategories, Preprint Mat. 8, The University of Trondheim, Norway, 1989.

    Google Scholar 

  4. Auslander, M. and Reiten, I.: Homologically Finite Subcategories, Preprint Mat. 7, The University of Trondheim, Norway, 1991.

    Google Scholar 

  5. Auslander, M. and Smalø, S.: Almost split sequence in subcategories, J. Algebra 69 (1981), 426–454; Addendum, J. Algebra 71 (1981), 592–594.9.

    Google Scholar 

  6. Dickson, S. E.: A torsion theory for abelian categories, Trans. Amer. Math. Soc. 121 (1965), 223–235.

    Google Scholar 

  7. Martínez-Villa, R.: Modules of dominant and codominant dimension, Comm. Algebra 20(12) (1992), 3515–3540.

    Google Scholar 

  8. Martínez-Villa, R.: Algebras of infinite dominant dimension, Tsukuba's Journal on Math. 18(1) (1994), 9–20.

    Google Scholar 

  9. Martínez-Villa, R.: Algebras of infinite dominant dimension and torsion theories, Comm. Algebra 22(11) (1994), 4519–4535.

    Google Scholar 

  10. Nakayama, T.: On algebra with complete homology, Abh. Sem. Hamburg 22 (1958), 300–307.

    Google Scholar 

  11. Stenström, B.: Rings of Quotients, Springer-Verlag, 1975.

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  1. Instituto de Matemáticas de la UNAM, Ciudad Universitaria, 04510, México D.F

    Roberto Martínez-Villa

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  1. Roberto Martínez-Villa
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Martínez-Villa, R. Contravariantly Finite Subcategories and Torsion Theories. Applied Categorical Structures 5, 321–337 (1997). https://doi.org/10.1023/A:1008698202018

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