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

Volume 136 / 2014

Stanisław Kasjan, Grzegorz Pastuszak Colloquium Mathematicum 136 (2014), 179-220 MSC: Primary 16G20; Secondary 16G60, 03C57, 06C05. DOI: 10.4064/cm136-2-3

Abstract

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.

Authors

  • Stanisław KasjanFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University
    87-100 Toruń, Poland
    e-mail
  • Grzegorz PastuszakCenter for Theoretical Physics of the
    Polish Academy of Sciences
    Al. Lotników 32/46
    02-668 Warszawa, Poland
    e-mail

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