On two tame algebras with super-decomposable pure-injective modules
Volume 123 / 2011
Colloquium Mathematicum 123 (2011), 249-276
MSC: Primary 16G20; Secondary 16G60, 03C60.
DOI: 10.4064/cm123-2-9
Abstract
Let $k$ be a field of characteristic different from 2. We consider two important tame non-polynomial growth algebras: the incidence $k$-algebra of the garland ${\mathcal G}_3$ of length 3 and the incidence $k$-algebra of the enlargement of the Nazarova–Zavadskij poset ${\mathcal N}{\mathcal Z}$ by a greatest element. We show that if $\Lambda $ is one of these algebras, then there exists a special family of pointed $\Lambda $-modules, called an independent pair of dense chains of pointed modules. Hence, by a result of Ziegler, $\Lambda $ admits a super-decomposable pure-injective module if $k$ is a countable field.
