ArticleOriginal scientific text
Title
Embeddings of Kronecker modules into the category of prinjective modules and the endomorphism ring problem
Authors 1, 2
Affiliations
- Fachbereich Mathematik und Informatik, Universität GH Essen, 45117 Essen, Germany
- Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Bibliography
- 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.
- S. Brenner, Decomposition properties of some small diagrams of modules, in: Symposia Math. 13, Academic Press, London, 1974, 127-141.
- A. L. S. Corner, Endomorphism algebras of large modules with distinguished submodules, J. Algebra 11 (1969), 155-185.
- Yu. A. Drozd, Matrix problems and categories of matrices, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 28 (1972), 144-153 (in Russian).
- 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.
- L. Fuchs, Large indecomposable modules in torsion theories, Aequationes Math. 34 (1987), 106-111.
- P. Gabriel, Indecomposable representations II, in: Symposia Math. 11, Academic Press, London, 1973, 81-104.
- R. Göbel and W. May, Four submodules suffice for realizing algebras over commutative rings, J. Pure Appl. Algebra 65 (1990), 29-43.
- 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.
- R. Göbel and D. Simson, Rigid families and endomorphism algebras of Kronecker modules, preprint, 1997.
- 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.
- S. Kasjan and D. Simson, Fully wild prinjective type of posets and their quadratic forms, J. Algebra 172 (1995), 506-529.
- S. Kasjan and D. Simson, A peak reduction functor for socle projective representations, ibid. 187 (1997), 49-70.
- 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.
- 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.
- C. M. Ringel, Representations of K-species and bimodules, J. Algebra 41 (1976), 269-302.
- C. M. Ringel, Infinite-dimensional representations of finite dimensional hereditary algebras, Symposia Math. 23 (1979), 321-412.
- C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, Berlin, 1984.
- S. Shelah, Infinite abelian groups, Whitehead problem and some constructions, Israel J. Math. 18 (1974), 243-256.
- D. Simson, Module categories and adjusted modules over traced rings, Dissertationes Math. 269 (1990).
- D. Simson, Peak reductions and waist reflection functors, Fund. Math. 137 (1991), 115-144.
- D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra Logic Appl. 4, Gordon and Breach, London, 1992.
- D. Simson, Posets of finite prinjective type and a class of orders, J. Pure Appl. Algebra 90 (1993), 71-103.
- D. Simson Triangles of modules and non-polynomial growth, C. R. Acad. Sci. Paris Sér. I 321 (1995), 33-38.
- 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.
- D. Simson, Prinjective modules, propartite modules, representations of bocses and lattices over orders, J. Math. Soc. Japan 49 (1997), 31-68.
- A. Skowroński, Minimal representation-infinite artin algebras, Math. Proc. Cambridge Philos. Soc. 116 (1994), 229-243.
- D. Vossieck, Représentations de bifoncteurs et interprétations en termes de modules, C. R. Acad. Sci. Paris Sér. I 307 (1988), 713-716.