Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On indecomposable modules over directed algebras


Author: Peter Dräxler
Journal: Proc. Amer. Math. Soc. 112 (1991), 321-327
MSC: Primary 16G60; Secondary 16D60
MathSciNet review: 1062830
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Generalizing a result of Bongartz we show that any nonsimple indecomposable module over a finite-dimensional $ k$-algebra $ A$ is an extension of an indecomposable and a simple module provided $ k$ is a field with more than two elements and $ A$ is representation directed. Our proof is based on fibre sums over simple modules and some known classification results on socle projective modules over peak algebras. In case the global dimension of $ A$ is at most 2 our methods also yield a description of the dimension vectors of the indecomposable $ A$-modules by the roots of the associated quadratic form.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16G60, 16D60

Retrieve articles in all journals with MSC: 16G60, 16D60


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1062830-X
PII: S 0002-9939(1991)1062830-X
Article copyright: © Copyright 1991 American Mathematical Society