Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

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 $2$-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


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google