The Gabriel-Roiter Measure and Some Applications
Người báo cáo: GS. Nguyen Viet Dung, Ohio University, USA

Thời gian: 9h, Thứ 4, ngày 8/3/2017
Địa điểm: Phòng số 6, nhà A14, Viện Toán học, 18 Hoàng Quốc Việt, Hà Nội
Tóm tắt: 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.

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