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The Gabriel–Roiter Measure for Right Pure Semisimple Rings

  • Nguyen Viet DungEmail author
  • Daniel Simson
Article

Abstract

We show how the Gabriel–Roiter measure, introduced by Ringel in (Bull Sci Math 129:726–748, 2005 and Contemp Math 406:105–135, 2006), applies to indecomposable modules of finite length over right pure semisimple rings, and in particular to the study of the open problem whether any right pure semisimple ring is of finite representation type.

Keywords

Right pure semisimple ring Finite representation type Gabriel–Roiter measure Auslander–Reiten quiver Preprojective module Preinjective module 

Mathematics Subject Classifications (2000)

16G10 16G60 16D70 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of MathematicsOhio University-ZanesvilleZanesvilleUSA
  2. 2.Faculty of Mathematics and InformaticsN. Copernicus UniversityToruńPoland

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