Abstract
This note is a short introduction to the concept of the Krull-Gabriel dimension of an algebra. We mention some recent results and give a list of open problems and conjectures.
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References
M. Auslander, Coherent functors, In: Proceedings of the conference on categorial algebra, La Jolla (1966), 189–231.
M. Auslander, Functors and morphisms determined by objects, In: Representation theory of algebras. Proc. Conf. Philadelphia 1976, (ed. R. Gordon), Dekker, New York (1978), 1–244.
M. Auslander, A functorial approach to representation theory, In: Representations of algebras (ed. M. Auslander, E. Luis), Springer Lecture Notes in Math. 944 (1980), 105–179.
K. Burke, M. Prest, The Ziegler and Zariski spectra of some domestic string algebras, Preprint (1998).
W.W. Crawley-Boevey, Tame algebras and bocses, Proc. London Math. Soc. 56 (1988), 451–483.
Yu. A. Drozd, Tame and wild matrix problems, In: Representation theory II, Springer Lecture Notes in Math. 832 (1980), 242–258.
P. Gabriel, Des catégories abéliennes, Bull. Soc. math. France 90 (1962), 323–448.
W. Geigle, The Krull-Gabriel dimension of the representation theory of a tame hereditary artin algebra and applications to the structure of exact sequences,Manuscripta Math. 54 (1985), 83–106.
W. Geigle, Krull dimension and artin algebras, In: Representation theory I, Finite dimensional algebras (ed. V. Dlab, P. Gabriel, G. Michler), Springer Lecture Notes in Math. 1177 (1984).
A. Grothendieck, Sur quelques poins d’algèbre homologique, Tôhoku Math. J., séries 2, 9 (1957), 119–221.
H. Krause, Generic modules over artin algebras, Proc. London Math. Soc. 76 (1998), 276–306.
H. Krause, The spectrum of a module category, Habilitationsschrift, Universitat Bielefeld (1998).
M. Prest, Model theory and modules, London Math. Soc. Lec. Note Series 130 (1988).
M. Prest, Morphisms between finitely presented modules and infinite-dimensional representations, Preprint (1996).
J. Schröer, On the Krull-Gabriel dimension of an algebra, Math. Z. (to appear), 19pp.
J. Schröer, On the infinite radical of a module category, Preprint (1998).
J.-P. Serre, Classes de groupes abeliens et groupes d’homotopie, Ann. of Math. 58 (1953), 258–294.
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Schröer, J. (2000). The Krull-Gabriel Dimension of an Algebra — Open Problems and Conjectures. 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_22
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DOI: https://doi.org/10.1007/978-3-0348-8426-6_22
Publisher Name: Birkhäuser, Basel
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