Embeddings of Kronecker modules into the category of prinjective modules and the endomorphism ring problem
Göbel, Rüdiger ; Simson, Daniel
Colloquium Mathematicae, Tome 78 (1998), p. 213-244 / Harvested from The Polish Digital Mathematics Library
Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:210540
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     author = {R\"udiger G\"obel and Daniel Simson},
     title = {Embeddings of Kronecker modules into the category of prinjective modules and the endomorphism ring problem},
     journal = {Colloquium Mathematicae},
     volume = {78},
     year = {1998},
     pages = {213-244},
     zbl = {0904.16007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv75z2p213bwm}
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Göbel, Rüdiger; Simson, Daniel. Embeddings of Kronecker modules into the category of prinjective modules and the endomorphism ring problem. Colloquium Mathematicae, Tome 78 (1998) pp. 213-244. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv75z2p213bwm/

[000] [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. | Zbl 0759.16006

[001] [2] S. Brenner, Decomposition properties of some small diagrams of modules, in: Symposia Math. 13, Academic Press, London, 1974, 127-141.

[002] [3] A. L. S. Corner, Endomorphism algebras of large modules with distinguished submodules, J. Algebra 11 (1969), 155-185. | Zbl 0214.05606

[003] [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).

[004] [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. | Zbl 0667.20045

[005] [6] L. Fuchs, Large indecomposable modules in torsion theories, Aequationes Math. 34 (1987), 106-111. | Zbl 0631.13010

[006] [7] P. Gabriel, Indecomposable representations II, in: Symposia Math. 11, Academic Press, London, 1973, 81-104.

[007] [8] R. Göbel and W. May, Four submodules suffice for realizing algebras over commutative rings, J. Pure Appl. Algebra 65 (1990), 29-43. | Zbl 0716.16015

[008] [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. | Zbl 0884.16017

[009] [10] R. Göbel and D. Simson, Rigid families and endomorphism algebras of Kronecker modules, preprint, 1997. | Zbl 0934.16024

[010] [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. | Zbl 0834.16010

[011] [12] S. Kasjan and D. Simson, Fully wild prinjective type of posets and their quadratic forms, J. Algebra 172 (1995), 506-529. | Zbl 0831.16010

[012] [13] S. Kasjan and D. Simson, A peak reduction functor for socle projective representations, ibid. 187 (1997), 49-70. | Zbl 0904.16008

[013] [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. | Zbl 0959.16012

[014] [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. | Zbl 0789.16010

[015] [16] C. M. Ringel, Representations of K-species and bimodules, J. Algebra 41 (1976), 269-302. | Zbl 0338.16011

[016] [17] C. M. Ringel, Infinite-dimensional representations of finite dimensional hereditary algebras, Symposia Math. 23 (1979), 321-412.

[017] [18] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, Berlin, 1984.

[018] [19] S. Shelah, Infinite abelian groups, Whitehead problem and some constructions, Israel J. Math. 18 (1974), 243-256. | Zbl 0318.02053

[019] [20] D. Simson, Module categories and adjusted modules over traced rings, Dissertationes Math. 269 (1990).

[020] [21] D. Simson, Peak reductions and waist reflection functors, Fund. Math. 137 (1991), 115-144. | Zbl 0780.16009

[021] [22] D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra Logic Appl. 4, Gordon and Breach, London, 1992. | Zbl 0818.16009

[022] [23] D. Simson, Posets of finite prinjective type and a class of orders, J. Pure Appl. Algebra 90 (1993), 71-103. | Zbl 0815.16006

[023] [24] D. Simson Triangles of modules and non-polynomial growth, C. R. Acad. Sci. Paris Sér. I 321 (1995), 33-38. | Zbl 0842.16010

[024] [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. | Zbl 0929.16014

[025] [26] D. Simson, Prinjective modules, propartite modules, representations of bocses and lattices over orders, J. Math. Soc. Japan 49 (1997), 31-68. | Zbl 0937.16019

[026] [27] A. Skowroński, Minimal representation-infinite artin algebras, Math. Proc. Cambridge Philos. Soc. 116 (1994), 229-243. | Zbl 0822.16010

[027] [28] D. Vossieck, Représentations de bifoncteurs et interprétations en termes de modules, C. R. Acad. Sci. Paris Sér. I 307 (1988), 713-716. | Zbl 0661.16025