Time: 9h00, Wednesday, March 8, 2017
Location: Room 4, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi

Abstract: P. Gabriel introduced in 1973 an invariant attached to finite length modules over algebras of bounded representation type, prompted by A.V. Roiter's proof in 1968 of the first Bauer-Thrall conjecture. Inspired by Roiter's and Gabriel's works ,  C.M. Ringel developed (around 2005) a theory of Gabriel-Roiter measures for finitely generated modules $M$ over an Artin algebra $R$, or more generally, for finite length modules $M$ over an arbitrary ring $R$. In this talk, we will present some basic results on the Gabriel-Roiter measure, and some of its applications in the classification of finitely generated indecomposable modules over Artinian rings. In particular, we will discuss the Gabriel-Roiter measures of indecomposable modules over left pure semisimple rings.