The Gabriel-Roiter submodules of simple homogeneous modules
- Autores: Bo Chen
- Localización: Proceedings of the American Mathematical Society, ISSN 0002-9939, Vol. 138, Nº 10, 2010, págs. 3415-3424
- Idioma: inglés
- DOI: 10.1090/s0002-9939-2010-10243-5
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Resumen
Let be a connected tame hereditary algebra over an algebraically closed field. We show that if is of type , , or , then every Gabriel-Roiter submodule of a quasi-simple module of rank (i.e. a simple homogeneous module) has defect . In particular, any Gabriel-Roiter submodule of a simple homogeneous module yields a Kronecker pair, and thus induces a full exact embedding of the category into , where is the Kronecker quiver. Consequently, we obtain that all quasi-simple modules are Gabriel-Roiter factor modules.
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