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On the existence of super-decomposable pure-injective modules over strongly simply connected algebras of non-polynomial growth

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Kasjan S., Pastuszak G.

Colloquium Mathematicum

2014

tom 136

nr 2

179-220

Assume that k is a field of characteristic different from 2. We show that if Γ is a strongly simply connected k-algebra of non-polynomial growth, then there exists a special family of pointed Γ-modules, called an independent pair of dense chains of pointed modules. Then it follows by a result of Ziegler that Γ admits a super-decomposable pure-injective module if k is a countable field.

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

100%

Kasjan S., Pastuszak G.

Colloquium Mathematicum

2011

tom 123

nr 2

249-276

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.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Kasjan S.

2 Pastuszak G.

1 2014

1 2011

Wyniki wyszukiwania

On the existence of super-decomposable pure-injective modules over strongly simply connected algebras of non-polynomial growth

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