Superdecomposable pure-injective modules exist over some string algebras

Puninski, Gena

doi:10.1090/S0002-9939-03-07292-7

Superdecomposable pure-injective modules exist over some string algebras
HTML articles powered by AMS MathViewer

by Gena Puninski PDF

Proc. Amer. Math. Soc. 132 (2004), 1891-1898 Request permission

Abstract:

We prove that over every non-domestic string algebra over a countable field there exists a superdecomposable pure-injective module.

References

Stefano Baratella and Mike Prest, Pure-injective modules over the dihedral algebras, Comm. Algebra 25 (1997), no. 1, 11–31. MR 1429745, DOI 10.1080/00927879708825836
M. C. R. Butler and Claus Michael Ringel, Auslander-Reiten sequences with few middle terms and applications to string algebras, Comm. Algebra 15 (1987), no. 1-2, 145–179. MR 876976, DOI 10.1080/00927878708823416
W. W. Crawley-Boevey, Maps between representations of zero-relation algebras, J. Algebra 126 (1989), no. 2, 259–263. MR 1024991, DOI 10.1016/0021-8693(89)90304-9
George Grätzer, General lattice theory, Lehrbücher und Monographien aus dem Gebiete der Exakten Wissenschaften, Mathematische Reihe, Band 52, Birkhäuser Verlag, Basel-Stuttgart, 1978. MR 504338, DOI 10.1007/978-3-0348-7633-9
Christian U. Jensen and Helmut 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 1057608
Mike Prest, Model theory and modules, London Mathematical Society Lecture Note Series, vol. 130, Cambridge University Press, Cambridge, 1988. MR 933092, DOI 10.1017/CBO9780511600562
Mike Prest, Morphisms between finitely presented modules and infinite-dimensional representations, Algebras and modules, II (Geiranger, 1996) CMS Conf. Proc., vol. 24, Amer. Math. Soc., Providence, RI, 1998, pp. 447–455. MR 1648645, DOI 10.2307/2586842
Claus Michael Ringel, The indecomposable representations of the dihedral $2$-groups, Math. Ann. 214 (1975), 19–34. MR 364426, DOI 10.1007/BF01428252
Claus Michael Ringel, Some algebraically compact modules. I, Abelian groups and modules (Padova, 1994) Math. Appl., vol. 343, Kluwer Acad. Publ., Dordrecht, 1995, pp. 419–439. MR 1378216
Claus Michael Ringel, Infinite length modules. Some examples as introduction, Infinite length modules (Bielefeld, 1998) Trends Math., Birkhäuser, Basel, 2000, pp. 1–73. MR 1789209, DOI 10.1007/978-3-0348-8426-6_{1}
J. Schröer, Hammocks for string algebras, Doctoral thesis, 1997.
Martin Ziegler, Model theory of modules, Ann. Pure Appl. Logic 26 (1984), no. 2, 149–213. MR 739577, DOI 10.1016/0168-0072(84)90014-9