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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:	Creators Email ORCID ORCID Put Code Chen, Bo UNSPECIFIED UNSPECIFIED UNSPECIFIED
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:	Keywords Language TAME HEREDITARY ALGEBRAS Multiple languages Mathematics, Applied; Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/49622