Module categories without short cycles are of finite type-Reference-Cited by-同舟云学术

Module categories without short cycles are of finite type

Published:1994 Issue:2 Volume:120 Page:371-375
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Happel Dieter,Liu Shi Ping

Abstract

Let A A be an artin algebra. An indecomposable finitely generated A A -module X X is said to be on a short cycle if there exists an indecomposable finitely generated A A -module Y Y and two nonzero noninvertible maps f : X → Y f:X \to Y and g : Y → X g:Y \to X . If there are no short cycles we show that there exist only finitely many indecomposable A A -modules up to isomorphism.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1994-120-02/S0002-9939-1994-1164144-9/S0002-9939-1994-1164144-9.pdf

Reference8 articles.

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3. Modules determined by their composition factors;Auslander, Maurice;Illinois J. Math.,1985

4. Vinberg’s characterization of Dynkin diagrams using subadditive functions with application to 𝐷𝑇𝑟-periodic modules;Happel, Dieter,1980

5. Directing projective modules;Happel, Dieter;Arch. Math. (Basel),1993

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