|
Superdecomposable pure-injective modules exist over some string algebras
Author(s):
Gena
Puninski
Journal:
Proc. Amer. Math. Soc.
132
(2004),
1891-1898.
MSC (2000):
Primary 16G20, 16D50
Posted:
December 18, 2003
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
We prove that over every non-domestic string algebra over a countable field there exists a superdecomposable pure-injective module.
References:
-
- 1.
- S. Baratella and M. Prest, Pure-injective modules over the dihedral algebras, Comm. Algebra, 25(1) (1997), 11-31. MR 98d:16021
- 2.
- M. Butler and C. M. Ringel, Auslander-Reiten sequences with few middle terms and applications to string algebras, Comm. Algebra, 15 (1-2) (1987), 145-179. MR 88a:16055
- 3.
- W. W. Crawley-Boevey, Maps between representations of zero-relation algebras, J. Algebra, 126 (1989), 259-263. MR 90k:16035
- 4.
- G. Grätzer, General Lattice Theory, Pure and Applied Mathematics, Vol. 75, Academic Press, New York, 1978. MR 80c:06001b
- 5.
- C. U. Jensen and H. Lenzing, Model-theoretic algebra with particular emphasis on fields, rings, modules, Algebra, Logic and Applications, Vol. 2, Gordon and Breach Science Publishers, New York, 1989. MR 91m:03038
- 6.
- M. Prest, Model Theory and Modules, London Math. Soc. Lecture Note Series, Vol. 130, Cambridge University Press, Cambridge, 1988. MR 89h:03061
- 7.
- M. Prest, Morphisms between finitely presented modules and infinite-dimensional representations, Canadian Math. Soc., Conference Proceedings, 24 (1998), pp. 447-455. MR 99i:16027
- 8.
- C. M. Ringel, The indecomposable representations of the dihedral
-groups, Math. Ann., 214 (1975), 19-34. MR 51:680 - 9.
- C. M. Ringel, Some algebraically compact modules. I, Abelian Groups and Modules, A. Facchini and C. Menini, eds., Kluwer, Dordrecht, 1995, pp. 419-439. MR 97c:16016
- 10.
- C. M. Ringel, Infinite length modules. Some examples as introduction, Infinite Length Modules, H. Krause and C. M. Ringel, eds., Trends in Math., Birkhäuser, Basel, 2000, pp. 1-73. MR 2002d:16002
- 11.
- J. Schröer, Hammocks for string algebras, Doctoral thesis, 1997.
- 12.
- M. Ziegler, Model theory of modules, Annals Pure Appl. Logic, 26 (1984), 149-213. MR 86c:03034
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
16G20, 16D50
Retrieve articles in all Journals with MSC
(2000):
16G20, 16D50
Additional Information:
Gena
Puninski
Affiliation:
Department of Mathematics, The Ohio State University at Lima, 4240, Campus Drive, Lima, Ohio 45804
Email:
puninskiy.1@osu.edu
DOI:
10.1090/S0002-9939-03-07292-7
PII:
S 0002-9939(03)07292-7
Keywords:
Pure-injective module,
string algebra,
superdecomposable module
Received by editor(s):
December 9, 2001
Received by editor(s) in revised form:
March 19, 2003
Posted:
December 18, 2003
Additional Notes:
This paper was written while the author visited the University of Manchester and was supported by EPSRC grant GR/R44942/01. He would like to thank the University for their kind hospitality
Communicated by:
Martin Lorenz
Copyright of article:
Copyright
2003,
American Mathematical Society
|