- J-STAGE home
- /
- Journal of the Mathematical So ...
- /
- Volume 39 (1987) Issue 4
- /
- Article overview
Brauer-Thrall type theorem for maximal Cohen-Macaulay modules
JOURNAL
FREE ACCESS
1987 Volume 39 Issue 4 Pages 719-739
Details
- Published: 1987 Received: June 02, 1986 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
-
Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M. Artin and J.-L. Verdier, Reflexive modules over rational double points, Math. Ann., 270 (1985), 79-82.
2) M. Auslander, Representation theory of artin algebras II, Comm. Algebra, 1 (1974), 269-310.
3) M. Auslander, Functors and morphisms determined by objects, Proc. Conf. Representation Theory, Philadelphia, 1976, Marcel Dekker, 1978, 1-244.
4) M. Auslander, Rational singularities and almost split sequences, Trans. Amer. Math. Soc., 293 (1986), 511-531.
5) M. Auslander, Isolated singularities and existence of almost split sequences, Proc. ICRA IV, Lecture Notes in Math., 1178 (1986), 194-241.
6) M. Auslander and M. Bridger, Stable module theory, Mem. Amer. Math. Soc., 94, 1969.
7) M. Auslander and I. Reiten, Representation theory of artin algebras III, Comm. Algebra, 3 (1975), 239-294.
8) M. Auslander and I. Reiten, Representation theory of artin algebras IV, Comm. Algebra, 5 (1977), 443-518.
9) M. Auslander and I. Reiten, Almost split sequences for rational double points, preprint.
10) R. Buchweitz, G. M. Greuel and F.-O. Schreyer, preprint, 1985.
11) E. Dieterich and A. Wiedemann, The Auslander-Reiten quiver of a simple curve singularity, Trans. Amer. Math. Soc., 294 (1986), 455-475.
12) E. G. Evans and P. Griffith, Syzygies, London Math. Soc. Lecture Note Series, 106, Cambridge Univ. Press, 1985.
13) G.-M. Greuel and H. Knörrer, Einfache Kurvesingularitaten und torsionfreie Moduln, Math. Ann., 270 (1985), 417-425.
14) J. Herzog, Ringe mit nur endlich vielen Isomorphieklassen von maximalen unzerlegbaren Cohen-Macaulay Moduln, Math. Ann., 233 (1978), 21-34.
15) J. Herzog and E. Kunz, Der kanonische Modul eines Cohen-Macaulay Rings, Lecture Notes in Math., 238, Springer-Verlag, 1971.
16) G. Hochschild, Cohomology groups of an associative algebra, Ann. of Math., 46 (1945), 58-67.
17) D. Happel, U. Preiser and C. M. Ringel, Vinberg's characterization of Dynkin diagrams using subadditive functions with application to DTr-periodic modules, Proc. ICRA II, Ottawa, Lecture Notes in Math., 832 (1980), 280-294.
18) M. Harada and Y. Sai, On categories of indecomposable modules I, Osaka J. Math., 8 (1971), 309-321.
19) H. Knörrer, Cohen-Macaulay modules on hypersurface singularities I, preprint, 1985.
20) K. Kiyek and G. Steinke, Einfach Kurvesingularitaten in beliebiger Charakteristik, Arch. Math., 45 (1985), 565-573.
21) H. Matsumura, Commutative algebra, Benjamin, New York, 1970.
22) M. Nagata, Local rings, Kriger, Huntington, 1975.
23) R. S. Pierce, Associative algebras, Graduate Texts in Math., 88, Springer-Verlag, 1982.
24) C. M. Ringel, Report on the Brauer-Thrall conjectures: Roiter's theorem and the theorem of Nazarova and Roiter, Proc. ICRA I, Ottawa, Lecture Notes in Math., 831 (1980), 104-136.
25) A. V. Roiter, Unbounded dimensionality of indecomposable representations of an algebra with an infinite number of indecomposable representations, Izv. Akad. Nauk SSSR, 32 (1968), 1275-1282.
26) G. Scheja and U. Storch, Differentialle Eigenschaften der Lokalisierungen analytischer Algebren, Math. Ann., 197 (1972), 137-170.
27) G. Scheja and U. Storch, Lokale Verzweigungstheorie, Schriftenreihe des Math. Inst. der Univ. Freiburg, 1974.
28) K. Yamagata, On artin rings of finite representation type, J. Algebra, 50 (1978), 276-283.
29) Y. Yoshino and T. Kawamoto, The fundamental module of a normal local domain of dimension 2, to appear in Trans. Amer. Math. Soc.
Right : [1] M. Artin and J. -L. Verdier, Reflexive modules over rational double points, Math. Ann., 270 (1985), 79-82.
[2] M. Auslander, Representation theory of artin algebras II, Comm. Algebra, 1 (1974), 269-310.
[3] M. Auslander, Functors and morphisms determined by objects, Proc. Conf. Representation Theory, Philadelphia, 1976, Marcel Dekker, 1978, 1-244.
[4] M. Auslander, Rational singularities and almost split sequences, Trans. Amer. Math. Soc., 293 (1986), 511-531.
[5] M. Auslander, Isolated singularities and existence of almost split sequences, Proc. ICRA IV, Lecture Notes in Math., 1178 (1986), 194-241.
[6] M. Auslander and M. Bridger, Stable module theory, Mem. Amer. Math. Soc., 94, 1969.
[7] M. Auslander and I. Reiten, Representation theory of artin algebras III, Comm. Algebra, 3 (1975), 239-294.
[8] M. Auslander and I. Reiten, Representation theory of artin algebras IV, Comm. Algebra, 5 (1977), 443-518.
[9] M. Auslander and I. Reiten, Almost split sequences for rational double points, preprint.
[10] R. Buchweitz, G. M. Greuel and F. -O. Schreyer, preprint, 1985.
[11] E. Dieterich and A. Wiedemann, The Auslander-Reiten quiver of a simple curve singularity, Trans. Amer. Math. Soc., 294 (1986), 455-475.
[12] E. G. Evans and P. Griffith, Syzygies, London Math. Soc. Lecture Note Series, 106, Cambridge Univ. Press, 1985.
[13] G. -M. Greuel and H. Knörrer, Einfache Kurvesingularitaten und torsionfreie Moduln, Math. Ann., 270 (1985), 417-425.
[14] J. Herzog, Ringe mit nur endlich vielen Isomorphieklassen von maximalen unzerlegbaren Cohen-Macaulay Moduln, Math. Ann., 233 (1978), 21-34.
[15] J. Herzog and E. Kunz, Der kanonische Modul eines Cohen-Macaulay Rings, Lecture Notes in Math., 238, Springer-Verlag, 1971.
[16] G. Hochschild, Cohomology groups of an associative algebra, Ann. of Math., 46 (1945), 58-67.
[17] D. Happel, U. Preiser and C. M. Ringel, Vinberg's characterization of Dynkin diagrams using subadditive functions with application to DTr-periodic modules, Proc. ICRA II, Ottawa, Lecture Notes in Math., 832 (1980), 280-294.
[18] M. Harada and Y. Sai, On categories of indecomposable modules I, Osaka J. Math., 8 (1971), 309-321.
[19] H. Knörrer, Cohen-Macaulay modules on hypersurface singularities I, preprint, 1985.
[20] K. Kiyek and G. Steinke, Einfach Kurvesingularitaten in beliebiger Charakteristik, Arch. Math., 45 (1985), 565-573.
[21] H. Matsumura, Commutative algebra, Benjamin, New York, 1970.
[22] M. Nagata, Local rings, Kriger, Huntington, 1975.
[23] R. S. Pierce, Associative algebras, Graduate Texts in Math., 88, Springer-Verlag, 1982.
[24] C. M. Ringel, Report on the Brauer-Thrall conjectures: Roiter's theorem and the theorem of Nazarova and Roiter, Proc. ICRA I, Ottawa, Lecture Notes in Math., 831 (1980), 104-136.
[25] A. V. Roiter, Unbounded dimensionality of indecomposable representations of an algebra with an infinite number of indecomposable representations, Izv. Akad. Nauk SSSR, 32 (1968), 1275-1282.
[26] G. Scheja and U. Storch, Differentialle Eigenschaften der Lokalisierungen analytischer Algebren, Math. Ann., 197 (1972), 137-170.
[27] G. Scheja and U. Storch, Lokale Verzweigungstheorie, Schriftenreihe des Math. Inst. der Univ. Freiburg, 1974.
[28] K. Yamagata, On artin rings of finite representation type, J. Algebra, 50 (1978), 276-283.
[29] Y. Yoshino and T. Kawamoto, The fundamental module of a normal local domain of dimension 2, to appear in Trans. Amer. Math. Soc.
Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -
Download PDF (1841K)
Download citation
RIS
BIB TEX
Text
How to download citation
Contact us
(compatible with EndNote, Reference Manager, ProCite, RefWorks)
(compatible with BibDesk, LaTeX)
Article 1st page
