Chen, Bo (2010). THE GABRIEL-ROITER SUBMODULES OF SIMPLE HOMOGENEOUS MODULES. Proc. Amer. Math. Soc., 138 (10). S. 3415 - 3425. PROVIDENCE: AMER MATHEMATICAL SOC. ISSN 0002-9939

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Abstract

Let Lambda be a connected tame hereditary algebra over an algebraically closed field. We show that if Lambda = kQ is of type (A) over tilde (n), (D) over tilde (n), (E) over tilde (6) or (E) over tilde (7), then every Gabriel-Roiter submodule of a quasi-simple module of rank I (i.e. a simple homogeneous module) has defect -1. 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 mod k (A) over tilde (1) into mod Lambda, where (A) over tilde (1) is the Kronecker quiver. Consequently, we obtain that all quasi-simple modules are Gabriel-Roiter factor modules.

Item Type: Journal Article
Creators:
CreatorsEmailORCIDORCID Put Code
Chen, BoUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-496229
DOI: 10.1090/S0002-9939-2010-10243-5
Journal or Publication Title: Proc. Amer. Math. Soc.
Volume: 138
Number: 10
Page Range: S. 3415 - 3425
Date: 2010
Publisher: AMER MATHEMATICAL SOC
Place of Publication: PROVIDENCE
ISSN: 0002-9939
Language: English
Faculty: Unspecified
Divisions: Unspecified
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
TAME HEREDITARY ALGEBRASMultiple languages
Mathematics, Applied; MathematicsMultiple languages
URI: http://kups.ub.uni-koeln.de/id/eprint/49622

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