Composition factors of indecomposable modules
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- by Maria Izabel Ramalho Martins
- Trans. Amer. Math. Soc. 350 (1998), 2009-2031
- DOI: https://doi.org/10.1090/S0002-9947-98-01929-1
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Abstract:
Let $\Lambda$ be a connected, basic finite dimensional algebra over an algebraically closed field. Our main aim is to prove that if $\Lambda$ is biserial, its ordinary quiver has no loop and every indecomposable $\Lambda$-module is uniquely determined by its composition factors, then each indecomposable $\Lambda$-module is multiplicity-free.References
- Olga Taussky, An algebraic property of Laplace’s differential equation, Quart. J. Math. Oxford Ser. 10 (1939), 99–103. MR 83, DOI 10.1093/qmath/os-10.1.99
- M. Auslander, Representation of algebras, notes of a course at Brandeis University, 1981.
- Maurice Auslander and Idun Reiten, Representation theory of Artin algebras. III. Almost split sequences, Comm. Algebra 3 (1975), 239–294. MR 379599, DOI 10.1080/00927877508822046
- Maurice Auslander and Idun Reiten, Representation theory of Artin algebras. V. Methods for computing almost split sequences and irreducible morphisms, Comm. Algebra 5 (1977), no. 5, 519–554. MR 439882, DOI 10.1080/00927877708822181
- Maurice Auslander and Idun Reiten, Modules determined by their composition factors, Illinois J. Math. 29 (1985), no. 2, 280–301. MR 784524
- Maurice Auslander, Idun Reiten, and Sverre O. Smalø, Representation theory of Artin algebras, Cambridge Studies in Advanced Mathematics, vol. 36, Cambridge University Press, Cambridge, 1995. MR 1314422, DOI 10.1017/CBO9780511623608
- Raymundo Bautista, On algebras of strongly unbounded representation type, Comment. Math. Helv. 60 (1985), no. 3, 392–399. MR 814146, DOI 10.1007/BF02567422
- C. Cibils, F. Larrión, and L. Salmerón, Métodos diagramáticos en teoría de representaciones, Monografías del Instituto de Matemáticas [Monographs of the Institute of Mathematics], vol. 11, Universidad Nacional Autónoma de México, Mexico City, 1982 (Spanish). MR 697231
- Peter Gabriel, Auslander-Reiten sequences and representation-finite algebras, Representation theory, I (Proc. Workshop, Carleton Univ., Ottawa, Ont., 1979), Lecture Notes in Math., vol. 831, Springer, Berlin, 1980, pp. 1–71. MR 607140
- Ma. I. R. Martins, Fatores de Composição de Módulos Indecomponíveis, Tese de doutoramento na Universidade de São Paulo, Brasil (1994), 107 páginas.
- L. A. Nazarova and A. V. Roĭter, Kategornye matrichnye zadachi i problema Brauèra-Trèlla, Izdat. “Naukova Dumka”, Kiev, 1973 (Russian). MR 0412233
- Zygmunt Pogorzały and Andrzej Skowroński, On algebras whose indecomposable modules are multiplicity-free, Proc. London Math. Soc. (3) 47 (1983), no. 3, 463–479. MR 716798, DOI 10.1112/plms/s3-47.3.463
- Claus Michael Ringel, On algorithms for solving vector space problems. I. Report on the Brauer-Thrall conjectures: Rojter’s theorem and the theorem of Nazarova and Rojter, Representation theory, I (Proc. Workshop, Carleton Univ., Ottawa, Ont., 1979), Lecture Notes in Math., vol. 831, Springer, Berlin, 1980, pp. 104–136. MR 607142
- Andrzej Skowroński and Josef Waschbüsch, Representation-finite biserial algebras, J. Reine Angew. Math. 345 (1983), 172–181. MR 717892
Bibliographic Information
- Maria Izabel Ramalho Martins
- Affiliation: Departamento de Matemática-IMEUSP, Universidade de São Paulo, CP 66281 - CEP 05315-970, São Paulo, Brazil
- Email: bel@ime.usp.br
- Received by editor(s): September 19, 1995
- Received by editor(s) in revised form: August 1, 1996
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 350 (1998), 2009-2031
- MSC (1991): Primary 16G20, 16G60
- DOI: https://doi.org/10.1090/S0002-9947-98-01929-1
- MathSciNet review: 1422900