Advertisement

Biserial rings

  • Kent R. Fuller
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 734)

Keywords

Finite Type Dynkin Diagram Serial Ring Indecomposable Module Primitive Idempotent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M. Auslander, Representation theory of artin algebras II, Comm. in Algebra 1(1974), 269–310.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    M. Auslander and M. Bridger, Stable module theory, Mem. Amer. Math. Soc. 94(1969).Google Scholar
  3. [3]
    M. Auslander, E.L. Green and I. Reiten, Modules with waists, Illinois J. Math. 19(1975), 467–478.MathSciNetzbMATHGoogle Scholar
  4. [4]
    G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloq. Publ. Vol. 25, 3rd Edition. Providence (1966).Google Scholar
  5. [5]
    V.P. Camillo, Distributive modules, J. Algebra 36(1975), 16–25.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    V. Dlab and C.M. Ringel, On algebras of finite representation type, J. Algebra 33(1975), 306–394.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    V. Dlab and C.M. Ringel, Indecomposable representations of graphs and algebras, Mem. Amer. Math. Soc. No. 173, 6(1976).Google Scholar
  8. [8]
    S.E. Dickson and K.R. Fuller, Algebras for which every indecomposable right module is invariant in its injective envelope, Pacific J. Math. 31(1969), 655–658.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    K.R. Fuller, On indecomposable injectives over artinian rings, Pacific J. Math. 29(1969), 115–135.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    K.R. Fuller, On a generalization of serial rings, Proc. of the Philadelphia Conference on Re. Thy., Dekker: Lect. Notes in Pure and Appl. Math. Vol. 37(1978), 359–368.MathSciNetGoogle Scholar
  11. [11]
    K.R. Fuller, Weakly symmetric rings of distributive module type, Comm. in Algebra 5(1977), 997–1008.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    K.R. Fuller, Rings of left invariant module type, Comm. in Algebra 6(1978), 153–167.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    K.R. Fuller and J. Haack, Rings with quivers that are trees, Pacific J. Math., to appear.Google Scholar
  14. [14]
    R. Gordon and E.L. Green, Modules with cores and amalgamations of indecomposable modules, Mem. Amer. Math. Soc. No. 187, 6(1976).Google Scholar
  15. [15]
    G.J. Janusz, Indecomposable modules for finite groups, Ann. of Math. 89(1969), 209–241.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    G.J. Janusz, Some left serial algebras of finite type, J. Algebra 23(1972), 404–411.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    W. Müller, On artin rings of finite representation type, Proceedings of the International Conference on Representations of Algebras, Carleton University. Springer-Verlag: Lecture Notes in Math. 488(1975).Google Scholar
  18. [18]
    T. Nakayama, On Frobeniusean algebras II, Ann. of Math. 42(1941), 1–22.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    T. Nakayama, Note on uniserial and generalized uniserial rings, Proc. Imp. Acad. Japan 16(1940), 285–289.CrossRefGoogle Scholar
  20. [20]
    M.I. Platzeck, Representation theory of algebras stably equivalent to an hereditary artin algebra, to appear.Google Scholar
  21. [21]
    M.I. Platzeck and M. Auslander, Representation theory of hereditary artin algebras, Proc. of the Philadelphia Conference on Rep. Thy., Dekker: Lect. Notes in Pure and Appl. Math., Vol. 37(1978), 389–424.MathSciNetzbMATHGoogle Scholar
  22. [22]
    I. Reiten, Amost split sequences for group algebras of finite representation type, to appear.Google Scholar
  23. [23]
    L.A. SKornjakov, When are all modules semi-chained?, Mat. Zametki 5(1969), 173–182.MathSciNetzbMATHGoogle Scholar
  24. [24]
    H. Tachikawa, On rings for which every indecomposable right module has a unique maximal submodule, Math. Z. 71(1959), 200–222.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    H. Tachikawa, On algebras of which every indecomposable representation has an irreducible one as the top or the bottom Loewy constituent, Math. Z. 75(1961), 215–227.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    R.B. Warfield, Jr., Serial rings and finitely presented modules, J. Algebra 37(1975), 187–222.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    M. Auslander, M.I. Platzeck and I. Reiten, Coxeter functors without diagrams, to appear.Google Scholar
  28. [28]
    J. Haack, Self-duality and serial rings, to appear.Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Kent R. Fuller
    • 1
  1. 1.The University of IowaIowa City

Personalised recommendations