C. Ringel

activity

20022026

most citedInvariant Subspaces of Nilpotent Linear Operators. I

91 citations · 386 across the 48 of their papers we have counts for

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Showing 2009 · math.RTShow all

4 papers · 2 filters

math.RT2009

Cluster-concealed algebras

Claus Michael Ringel

The cluster-tilted algebras have been introduced by Buan, Marsh and Reiten, they are the endomorphism rings of cluster-tilting objects $T$ in cluster categories; we call such an al…

math.RT2009

Gabriel-Roiter inclusions and Auslander-Reiten theory

Claus Michael Ringel

Let $Λ$ be an artin algebra. The aim of this paper is to outline a strong relationship between the Gabriel-Roiter inclusions and the Auslander-Reiten theory. If $X$ is a Gabriel-Ro…

math.RT2009

Iyama's finiteness theorem via strongly quasi-hereditary algebras

Claus Michael Ringel

Let $Λ$ be an artin algebra and $X$ a finitely generated $Λ$ -module. Iyama has shown that there exists a module $Y$ such that the endomorphism ring $Γ$ of $X \oplus Y$ is quasi-here…

math.RT2009

Indecomposables live in all smaller lengths

Claus Michael Ringel

Let $Λ$ be a finite-dimensional $k$ -algebra with $k$ algebraically closed. Bongartz has recently shown that the existence of an indecomposable $Λ$ -module of length $n > 1$ implies…