On two tame algebras with super-decomposable pure-injective modules

Stanisław Kasjan¹ ; Grzegorz Pastuszak¹

¹ Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland

Colloquium Mathematicum, Tome 123 (2011) no. 2, pp. 249-276

Résumé

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.

Détail

DOI : 10.4064/cm123-2-9

Keywords: field characteristic different consider important tame non polynomial growth algebras incidence k algebra garland mathcal length incidence k algebra enlargement nazarova zavadskij poset mathcal mathcal greatest element lambda these algebras there exists special family pointed lambda modules called independent pair dense chains pointed modules hence result ziegler lambda admits super decomposable pure injective module countable field