Skip to main content
SpringerLink
Log in

Report on the Brauer-Thrall conjectures: Rojter's theorem and the theorem of Nazarova and Rojter (on algorithms for solving vectorspace problems. I)

  • Chapter
  • First Online:
Representation Theory I

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 831))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Auslander, M.: Representation theory of Artin algebras II, Comm. Algebra 2 (1974), 269–310

    Article  MathSciNet  MATH  Google Scholar 

  2. Auslander, M.: Applications of morphisms determined by objects. Proc. Conf. on Representation Theory. Philadelphia (1976) Marcel Dekker (1978), 245–327

    Google Scholar 

  3. Auslander, M.; Reiten, I.: Representation theory of Artin algebras III. Comm. Algebra 3 (1975), 239–294, IV. Comm. Algebra 5 (1977), 443–518

    Article  MathSciNet  MATH  Google Scholar 

  4. Auslander, M.; Smalø, S.O.: Preprojective modules over Artin algebras. To appear

    Google Scholar 

  5. Bashev, V.A.: Representations of the ℤ2×ℤ2 group in the field of characteristic 2. Dokl. Akad. Nauk 141 (1961), 1015–1018

    MathSciNet  Google Scholar 

  6. Bautista, R.: Irreducible maps and the radical of a category. To appear

    Google Scholar 

  7. Brauer, R.: On the indecomposable representations of algebras. Bull. Amer. Math. Soc. 47 (1941), Abstract 334, p. 684

    Google Scholar 

  8. Brenner, S.: Quivers with commutativity conditions and some phenomenology of forms. In: Representations of Algebras. Springer LNM 488 (1975), 29–53

    Article  MATH  Google Scholar 

  9. Brummund, H.: Über Gruppenringe mit einem Koeffizientenkörper der Charakteristik p. Dissertation Münster 1939.

    Google Scholar 

  10. Cohn, P.M.: Free rings and their relations. Academic Press 1971

    Google Scholar 

  11. Cozzens, J.H.: Homological properties of the ring of differential polynomials. Bull. Amer. Math. Soc. 76 (1970), 75–79

    Article  MathSciNet  MATH  Google Scholar 

  12. Dlab, V.; Ringel, C.M.: On algebras of finite representation type. J. Algebra 33 (1975), 306–394

    Article  MathSciNet  MATH  Google Scholar 

  13. Dlab, V.; Ringel, C.M.: Indecomposable representations of graphs and algebras. Memoirs. Amer. Math. Soc. 173 (1976)

    Google Scholar 

  14. Donovan, P.; Freislich, M.R.: Some evidence for an extension of the Brauer-Thrall conjecture. Unpublished (1973)

    Google Scholar 

  15. Drozd, Ju.A.: Representations of commutative algebras. Funkc. Anal. i Prilozen 6(4) (1972), 41–43. Engl. transl. Funct. Anal. Appl. 6 (1972), 286–288

    MathSciNet  Google Scholar 

  16. Drozd, Ju.A.: On tame and wild matrix problems. Matrix problems Kiev (1977), 104–114

    Google Scholar 

  17. Gabriel, P.: Unzerlegbare Darstellungen I. Manuscripta Math. 6 (1972) 71–103

    Article  MathSciNet  MATH  Google Scholar 

  18. Gabriel, P.: Indecomposable representations II. Symp. Math. Ist. Naz. Alta Mat. 11 (1973), 81–104

    MathSciNet  MATH  Google Scholar 

  19. Gabriel, P.: Problèmes actuels de théorie des représentations. Enseignement Math. 20 (1974), 323–332

    MathSciNet  MATH  Google Scholar 

  20. Gabriel, P.: Trends in representation theory. Report at the workshop. Ottawa 1979

    Google Scholar 

  21. Harada, M.; Sai, Y.: On categories of indecomposable modules I. Osaka J. Math. 7 (1970), 323–344

    MathSciNet  MATH  Google Scholar 

  22. Heller, A.; Reiner, I.: Indecomposable representations. III. J. Math. 5 (1961), 314–323

    MathSciNet  MATH  Google Scholar 

  23. Jans, J.P.: On the indecomposable representations of algebras Annals Math. 66 (1957), 418–429

    Article  MathSciNet  MATH  Google Scholar 

  24. Kelly, G.M.: The radical of a category. J. Austr. Math. Soc. 4 (1964), 299–307

    Article  MathSciNet  MATH  Google Scholar 

  25. Kleiner, M.M.: Partially ordered sets of finite type Zap. Naučn. Sem.LOMI 28 (1972), 32–41 Engl. transl.: J. Soviet Math. 23 (1975), 607–615

    MathSciNet  MATH  Google Scholar 

  26. Kleiner, M.M.: On exact representations of partially ordered sets of finite representation type. Zap. Naučn. Sem. LOMI 28 (1972), 42–60., Engl. Transl.: J. Soviet Math. 23 (1975), 616–628

    MathSciNet  Google Scholar 

  27. Kleiner, M.M.: in: 3. Symp. on rings, algebras and modules. Tartu (1976).

    Google Scholar 

  28. Köthe, G.: Verallgemeinerte abelsche Gruppen mit hyperkomplexen Operatorring. Math. Z. 39 (1934)

    Google Scholar 

  29. Koifman, L.A.: Rings over which every module has a maximal submodule. Mat. Zam 7(3) (1970), 359–367 Engl. transl. Math. Notes: Acad. Sc. USSR 7 (1970), 215–219

    MathSciNet  Google Scholar 

  30. Nakayama, T.: Note on uniserial and generalized uniserial rings. Proc. Imp. Acad. Tokyo 16 (1940), 285–289

    Article  MathSciNet  Google Scholar 

  31. Nazarova, L.A.; Rojter, A.V.: Representations of partially ordered sets. Zap. Naučn. Sem. LOMI 28 (1972), 5–31 Engl. transl.: J. Soviet Math. 23 (1975), 585–606

    MathSciNet  MATH  Google Scholar 

  32. Nazarova, L.A.: Rojter, A.V.: Categorical matrix problems and the Brauer-Thrall conjecture. Preprint. Inst. Math. Acad. Sci., Kiev 1973, German transl. Mitt. Math. Sem. Gießen 115 (1975)

    Google Scholar 

  33. Riedtmann, Chr.: Algebren, Darstellungsköcher, Überlagerungen und zurück. To appear in Comm. Helv.

    Google Scholar 

  34. Ringel, C.M.: Representations of K-species and bimodules. J. Algebra 41 (1976), 269–302

    Article  MathSciNet  MATH  Google Scholar 

  35. Ringel, C.M.: Tame algebras. Algorithms for solving vector space problems II. These proceedings

    Google Scholar 

  36. Rojter, A.V.: The unboundedness of the dimension of the indecomposable representations of algebras that have a finite number of indecomposable representations. Izv. Acad. Nauk SSR, 32 (1968), 1275–1282

    Google Scholar 

  37. Smalø, S.O.: The inductive step of the second Brauer-Thrall conjecture. To appear in Can. J. Math.

    Google Scholar 

  38. Thrall, R.M.: On ahdir algebras. Bull. Amer. Math. Soc. 53 (1947) Abstract 22, p. 49

    Google Scholar 

  39. Thrall, R.M.: On a Galois connection between algebras of linear transformations and lattices of subspaces of a vectorspace. Can. J. Math. 4 (1952), 227–239

    Article  MathSciNet  MATH  Google Scholar 

  40. Thrall, R.M.; Duncan, D.G.: Note on free modular lattices. Amer. J. Math. 75 (1953), 627–632

    Article  MathSciNet  MATH  Google Scholar 

  41. Yamagata, K.: On artinian rings of finite representation type. J. Algebra 50 (1978), 276–283

    Article  MathSciNet  MATH  Google Scholar 

  42. Yoshii, T.: On algebras of bounded representation type. Osaka Math. J. 8 (1956), 51–105

    MathSciNet  MATH  Google Scholar 

  43. Yoshii, T.: Note on algebras of strongly unbounded representation type. Proc. Japan. Acad. 32 (1956), 383–387

    Article  MathSciNet  MATH  Google Scholar 

  44. Yoshii, T.: Note on algebras of bounded representation type. Proc. Japan. Acad. 32 (1956), 441–445.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, D-4800, Bielefeld, Germany

    Claus Michael Ringel

Authors
  1. Claus Michael Ringel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Vlastimil Dlab Peter Gabriel

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag

About this chapter

Cite this chapter

Ringel, C.M. (1980). Report on the Brauer-Thrall conjectures: Rojter's theorem and the theorem of Nazarova and Rojter (on algorithms for solving vectorspace problems. I). In: Dlab, V., Gabriel, P. (eds) Representation Theory I. Lecture Notes in Mathematics, vol 831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089780

Download citation

  • DOI: https://doi.org/10.1007/BFb0089780

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10263-2

  • Online ISBN: 978-3-540-38385-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation