The Gabriel-Roiter
measure and some applications.
by
Nguyen Viet Dung
(Ohio University - Zanesville)
Recently C. M. Ringel introduced the Gabriel-Roiter measure,
which is an invariant attached to finite length modules over any ring
or algebra. The concept was motivated by works of Gabriel and Roiter
over 30 years ago in the context of algebras of bounded representation
type and the first Brauer-Thrall conjecture. We will give an
introduction to Ringel's work, in particular the application of the
Gabriel-Roiter measure for giving new proofs of some classical results
of representation theory of Artinian rings and algebras. We will also
discuss our joint work with D. Simson on this subject.