On the existence of super-decomposable pure-injective modules over strongly simply connected algebras of non-polynomial growth
Tom 136 / 2014
Colloquium Mathematicum 136 (2014), 179-220 MSC: Primary 16G20; Secondary 16G60, 03C57, 06C05. DOI: 10.4064/cm136-2-3
Assume that $k$ is a field of characteristic different from 2. We show that if $\varGamma $ is a strongly simply connected $k$-algebra of non-polynomial growth, then there exists a special family of pointed $\varGamma $-modules, called an independent pair of dense chains of pointed modules. Then it follows by a result of Ziegler that $\varGamma $ admits a super-decomposable pure-injective module if $k$ is a countable field.