6 problems

A string algebra is an algebra of the form $A=\Bbbk Q/I$ whose admissible ideal $I$ is generated by relations in the bound quiver, and a SUMP algebra is a string algebra with the U…

Stable-rank bound. The stable rank of $\Lambda$ is strictly bounded above by $\omega^2$.

Let $A$ be a domestic string algebra. The constructions described by Ringel for string algebras produce indecomposable pure-injective $A$-modules. Domestic string algebra classific…

Unique-maximal-path conjecture. Every arrow of $Q$ belongs to a unique maximal path.

Schröer's conjecture. The Krull–Gabriel dimension of $R$ equals

Let $A$ be a domestic string algebra, and let $M$ be an infinite-dimensional indecomposable pure injective $A$-module. An infinite-dimensional band module means a Pr"ufer, adic, or…