Abstract
This paper presents a streamlined proof of a theorem of H. Krause [8] regarding subsequent improvements by Krause and G. Zwara [10]. Our account is a revised version of a mini-course given at the Euroconference “Homological Invariants in Representation Theory” in Ioannina, March 1999. We include necessary background on infinite dimensional modules and functor categories centered around the concept of purity.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Bass. Finitistic dimension and a homological generalization of simiprimary rings. Trans. Amer. Math. Soc. 95, 466–488 (1960).
W. Crawley-Boevey. Tame algebras and generic modules. Proc. London Math. Soc. 63 (1991), 241–265.
W. Crawley-Boevey. Locally finitely presented additive categories. Commun. Algebra. 22 (1994), 1641–1674.
P. Gabriel. Des catégories abéliennes. Bull. Soc. Math. France. 90 (1962), 323–448.
L. Gruson and C. U. Jensen. Modules algébriquement compacts et foncteures \({{\mathop{{\lim }}\limits_{ \leftarrow } }^{{\left( i \right)}}} \). C. R. Acad. Sci. Paris Sér. A-B 276 (1973), A1651–A1653.
L. Gruson and C. U. Jensen. Deux applications de la notion de L-dimension. C. R. Acad. Sci. Paris Sér. A-B 282 (1976), A23–A24.
C.U. Jensen and H. Lenzing. Model Theoretic Algebra, Gordon and Breach Science Publishers, 1989.
H. Krause. Stable equivalence preserves representation type. Comment. Math. Hein. 72 (1997), 266–284.
H. Krause. Exactly definable categories. J. Algebra. 201 (1998), 456–492.
H. Krause and G. Zwara. Stable equivalence and generic modules. Preprint Series of SFB 343, Bielefeld. 98–119, 1998.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Basel AG
About this paper
Cite this paper
Lenzing, H. (2000). Invariance of Tameness under Stable Equivalence: Krause’s Theorem. In: Krause, H., Ringel, C.M. (eds) Infinite Length Modules. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8426-6_21
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8426-6_21
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9562-0
Online ISBN: 978-3-0348-8426-6
eBook Packages: Springer Book Archive