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 𝒢₃ of length 3 and the incidence k-algebra of the enlargement of the Nazarova-Zavadskij poset 𝒩 𝓩 by a greatest element. We show that if Λ is one of these algebras, then there exists a special family of pointed Λ-modules, called an independent pair of dense chains of pointed modules. Hence, by a result of Ziegler, Λ admits a super-decomposable pure-injective module if k is a countable field.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-2-9,
author = {Stanis\l aw Kasjan and Grzegorz Pastuszak},
title = {On two tame algebras with super-decomposable pure-injective modules},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {249-276},
zbl = {1257.16013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-2-9}
}
Stanisław Kasjan; Grzegorz Pastuszak. On two tame algebras with super-decomposable pure-injective modules. Colloquium Mathematicae, Tome 122 (2011) pp. 249-276. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-2-9/