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# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## 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

#### Streszczenie

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.

#### Autorzy

• Stanisław KasjanFaculty of Mathematics and Computer Science
Nicolaus Copernicus University
87-100 Toruń, Poland
e-mail
• Grzegorz PastuszakCenter for Theoretical Physics of the