ArticleOriginal scientific text

Title

Embeddings of Kronecker modules into the category of prinjective modules and the endomorphism ring problem

Authors 1, 2

Affiliations

  1. Fachbereich Mathematik und Informatik, Universität GH Essen, 45117 Essen, Germany
  2. Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Bibliography

  1. C. Böttinger and R. Göbel, Endomorphism algebras of modules with distinguished partially ordered submodules over commutative rings, J. Pure Appl. Algebra 76 (1991), 121-141.
  2. S. Brenner, Decomposition properties of some small diagrams of modules, in: Symposia Math. 13, Academic Press, London, 1974, 127-141.
  3. A. L. S. Corner, Endomorphism algebras of large modules with distinguished submodules, J. Algebra 11 (1969), 155-185.
  4. Yu. A. Drozd, Matrix problems and categories of matrices, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 28 (1972), 144-153 (in Russian).
  5. B. Franzen and R. Göbel, The Brenner-Butler-Corner-Theorem and its applications to modules, in: Abelian Group Theory, Gordon and Breach, London, 1986, 209-227.
  6. L. Fuchs, Large indecomposable modules in torsion theories, Aequationes Math. 34 (1987), 106-111.
  7. P. Gabriel, Indecomposable representations II, in: Symposia Math. 11, Academic Press, London, 1973, 81-104.
  8. R. Göbel and W. May, Four submodules suffice for realizing algebras over commutative rings, J. Pure Appl. Algebra 65 (1990), 29-43.
  9. R. Göbel and W. May, Endomorphism algebras of peak I-spaces over posets of infinite prinjective type, Trans. Amer. Math. Soc. 349 (1997), 3535-3567.
  10. R. Göbel and D. Simson, Rigid families and endomorphism algebras of Kronecker modules, preprint, 1997.
  11. S. Kasjan and D. Simson, Varieties of poset representations and minimal posets of wild prinjective type, in: Proc. Sixth Internat. Conf. Representations of Algebras, CMS Conf. Proc. 14, 1993, 245-284.
  12. S. Kasjan and D. Simson, Fully wild prinjective type of posets and their quadratic forms, J. Algebra 172 (1995), 506-529.
  13. S. Kasjan and D. Simson, A peak reduction functor for socle projective representations, ibid. 187 (1997), 49-70.
  14. S. Kasjan and D. Simson, A subbimodule reduction, a peak reduction functor and tame prinjective type, Bull. Polish Acad. Sci. Math. 45 (1997), 89-107.
  15. J. A. de la Pe na and D. Simson, Prinjective modules, reflection functors, quadratic forms and Auslander-Reiten sequences, Trans. Amer. Math. Soc. 329 (1992), 733-753.
  16. C. M. Ringel, Representations of K-species and bimodules, J. Algebra 41 (1976), 269-302.
  17. C. M. Ringel, Infinite-dimensional representations of finite dimensional hereditary algebras, Symposia Math. 23 (1979), 321-412.
  18. C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, Berlin, 1984.
  19. S. Shelah, Infinite abelian groups, Whitehead problem and some constructions, Israel J. Math. 18 (1974), 243-256.
  20. D. Simson, Module categories and adjusted modules over traced rings, Dissertationes Math. 269 (1990).
  21. D. Simson, Peak reductions and waist reflection functors, Fund. Math. 137 (1991), 115-144.
  22. D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra Logic Appl. 4, Gordon and Breach, London, 1992.
  23. D. Simson, Posets of finite prinjective type and a class of orders, J. Pure Appl. Algebra 90 (1993), 71-103.
  24. D. Simson Triangles of modules and non-polynomial growth, C. R. Acad. Sci. Paris Sér. I 321 (1995), 33-38.
  25. D. Simson, Representation embedding problems, categories of extensions and prinjective modules, in: Proc. Seventh Internat. Conf. Representations of Algebras, CMS Conf. Proc. 18, 1996, 601-639.
  26. D. Simson, Prinjective modules, propartite modules, representations of bocses and lattices over orders, J. Math. Soc. Japan 49 (1997), 31-68.
  27. A. Skowroński, Minimal representation-infinite artin algebras, Math. Proc. Cambridge Philos. Soc. 116 (1994), 229-243.
  28. D. Vossieck, Représentations de bifoncteurs et interprétations en termes de modules, C. R. Acad. Sci. Paris Sér. I 307 (1988), 713-716.
Pages:
213-244
Main language of publication
English
Received
1997-01-02
Accepted
1997-02-20
Published
1998
Exact and natural sciences