Abstract
Let R be a hereditary finite-dimensional algebra of tame type. In this note it is shown that any pure-injective R-module contains an indecomposable direct summand. This result is used to prove that if R is not countable and the category of R-modules contains a full sub-category equivalent to the category of representations of Ã1 then R is not pure-hereditary.
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© 1980 Springer-Verlag
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Okoh, F. (1980). Hereditary algebras that are not pure-hereditary. In: Dlab, V., Gabriel, P. (eds) Representation Theory II. Lecture Notes in Mathematics, vol 832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088477
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DOI: https://doi.org/10.1007/BFb0088477
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