Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Short chains and regular components

Authors: Idun Reiten, Andrzej Skowroński and Sverre O. Smalø
Journal: Proc. Amer. Math. Soc. 117 (1993), 601-612
MSC: Primary 16G70; Secondary 16G10, 16G60
MathSciNet review: 1124149
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \Lambda $ be a finite-dimensional $ k$-algebra with $ k$ an algebraically closed field and $ \operatorname{ind} \Lambda $ a chosen subcategory of a complete set of isomorphism classes of finitely generated indecomposable $ \Lambda $-modules. This paper deals with the regular components of $ \operatorname{ind} \Lambda $ consisting of modules that are not the middle of any short chain. It is proved that the number of such components containing only a finite number of $ DTr$-orbits is finite. Further, the infinite radical of such a component is zero and the component is isomorphic to the mesh category of its underlying translation quiver. Families of selfinjective algebras having such components are constructed.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16G70, 16G10, 16G60

Retrieve articles in all journals with MSC: 16G70, 16G10, 16G60

Additional Information

Article copyright: © Copyright 1993 American Mathematical Society