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Representations of trivial extensions of hereditary algebras

  • Hiroyuki Tachikawa
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 832)

Keywords

Direct Summand Projective Cover Trivial Extension Artin Algebra Hereditary Algebra 
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References

  1. [1]
    Auslander, M. and Reiten, I.: Representation theory of artin algebras III; almost split sequences. Comm. in Algebra 3, 239–294 (1975).MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    Brenner, S. and Butler, M. C. R.: The equivalence of certain functors occuring in the representation theory of artin algebras and species, J. London Math. Soc. (2) 14, 183–187 (1976).MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Dlab, V. and Ringel, C. M.: On algebras of finite representation type, J. Algebra 33, 306–394 (1975).MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Dlab, V. and Ringel, C. M.: Representations of graphs and algebras, Memoirs Amer. Math. Soc. 173, Providence (1976).Google Scholar
  5. [5]
    Dlab, V. and Ringel, C. M.: The representations of tame hereditary algebras, Lecture notes in pure and applied math. 37 (Proc. Philadelphia Conf.), 329–353 (1976).Google Scholar
  6. [6]
    Fossum, R. M., Griffith, P. A. and Reiten, I: Trivial extensions of abelian categories, Lecture notes in math. 456, Berlin-Heidelberg-New York: Springer (1975).zbMATHGoogle Scholar
  7. [7]
    Gabriel, P.: Indecomposable representations II, Symposia Mathematica, Vol. XI, Academic Press, New york/San Francisco/London, 81–104 (1973).Google Scholar
  8. [8]
    Green, E. L. and Reiten, I: On the construction of ring extensions, Glasgow Math. J. 17, 1–11 (1976).MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    Müller, W.: Unzerlegbare Moduln über Artinschen Ringen, Math. Z. 137, 197–226 (1974).MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Platzeck, M. T. and Auslander, M.: Representation theory of hereditary artin algebras, Lecture notes in pure and applied math. 37 (Proc. Phildelphia conf.), 389–353 (1976).Google Scholar
  11. [11]
    Ringel, C. M.: Representations of K-species and bimodules, J. Algebra 41, 269–302(1976).MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    Ringel, C. M.: Finite dimensional hereditary algebras of wild representation type (to appear).Google Scholar
  13. [13]
    Tachikawa, H.: Trivial extensions of finite representation type, Proc. Symp. on Representations of groups and algebras, University of Tsukuba, Ibaraki, 69–80 (1978) (In Japanese).Google Scholar
  14. [14]
    Wakamatsu, T.: Trivial extensions of Artin algebras (to appear)Google Scholar
  15. [15]
    Yamagata, K: Extensions over hereditary artinian rings with self-dualities 1 (to appear).Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Hiroyuki Tachikawa

There are no affiliations available

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