Archiv der Mathematik

, Volume 50, Issue 2, pp 128–133 | Cite as

Modules of bounded length in Auslander-Reiten components

  • Eugenia Marmolejo
  • Claus Michael Ringel


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. Auslander, R. Bautista, M. I. Platzeck, I. Reiten andS. O. Smalø, Almost split sequences whose middle term has at most two indecomposable summands. Canad. J. Math.31, 942–960 (1979).Google Scholar
  2. [2]
    K. Bongartz, On a result of Bautista and Smalø on cycles. Comm. Algebra11, 2123–2124 (1983).Google Scholar
  3. [3]
    M. C. R. Butler andC. M. Ringel, Auslander-Reiten sequences with few middle terms, with applications to string algebras. Comm. Algebra15, 145–179 (1987).Google Scholar
  4. [4]
    R. Bautista andS. O. Smalø, Nonexistent cycles. Comm. Algebra11, 1755–1767 (1983).Google Scholar
  5. [5]
    D. Happel, U. Preiser andC. M. Ringel, Vinberg's characterization of Dynkin diagrams using subadditive functions with application to DTr-periodic modules. LNM832, 280–294, Berlin-Heidelberg-New York 1980.Google Scholar
  6. [6]
    M. Harada andY. Sai, On categories of indecomposable modules I. Osaka J. Math.7, 323–344 (1970).Google Scholar
  7. [7]
    M. Hoshino, Splitting torsion theories induced by tilting modules. Comm. Algebra11, 427–441 (1983).Google Scholar
  8. [8]
    K. Igusa andG. Todorov, A characterization of finite Auslander-Reiten quivers. J. Algebra89, 148–177 (1984).Google Scholar
  9. [9]
    Chr. Riedtmann, Algebren, Darstellungsköcher, Überlagerungen und zurück. Comment. Math. Helv.55, 199–224 (1980).Google Scholar
  10. [10]
    C. M. Ringel, Report on the Brauer-Thrall conjectures. LNM831, 104–136, Berlin-Heidelberg-New York 1980.Google Scholar
  11. [11]
    C. M.Ringel, Tame algebras and integral quadratic forms. LNM1099, Berlin-Heidelberg-New York 1984.Google Scholar
  12. [12]
    C. M. Ringel, Representation theory of finite dimensional algebras. Durham lectures. In: Representations of Algebras. London Math. Soc. Lecture Note Series.116, 7–79 (1986).Google Scholar
  13. [13]
    C. M.Ringel, The regular components of the Auslander-Reiten quiver of a tilted algebra. To appear in Chinese Ann. Math.Google Scholar

Copyright information

© Birkhäuser Verlag 1988

Authors and Affiliations

  • Eugenia Marmolejo
    • 1
  • Claus Michael Ringel
    • 1
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeld 1

Personalised recommendations