Modules with irrational slope over tubular algebras

Abstract

Let $A$ be a tubular algebra and let $r$ be a positive irrational. Let ${\mathcal{D}}_r$ be the definable subcategory of $A$-modules of slope $r$. Then the width of the lattice of pp formulas for ${\mathcal{D}}_r$ is $\infty$. It follows that if $A$ is countable then there is a superdecomposable pure-injective module of slope $r$.

minor corrections/improvements to arguments

Cited by in corpus (2)

• Tilting and cotilting modules over concealed canonical algebras
• Decidability of theories of modules over tubular algebras