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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Telescope conjecture, idempotent ideals, and the transfinite radical


Author: Jan Stovícek
Journal: Trans. Amer. Math. Soc. 362 (2010), 1475-1489
MSC (2000): Primary 18E35; Secondary 16E30, 16G60
Published electronically: October 9, 2009
MathSciNet review: 2563737
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Abstract: We show that for an artin algebra $ \Lambda$, the telescope conjecture for module categories is equivalent to certain idempotent ideals of $ \operatorname{mod}\Lambda$ being generated by identity morphisms. As a consequence, we prove the conjecture for domestic standard selfinjective algebras and domestic special biserial algebras. We achieve this by showing that in any Krull-Schmidt category with local d.c.c. on ideals, any idempotent ideal is generated by identity maps and maps from the transfinite radical.


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Additional Information

Jan Stovícek
Affiliation: Institutt for matematiske fag, Norges teknisk-naturvitenskapelige universitet, N-7491 Trondheim, Norway
Address at time of publication: Faculty of Mathematics and Physics, Department of Algebra, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic
Email: stovicek@math.ntnu.no, stovicek@karlin.mff.cuni.cz

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04812-0
PII: S 0002-9947(09)04812-0
Keywords: Telescope conjecture, idempotent ideals, transfinite radical
Received by editor(s): February 6, 2008
Published electronically: October 9, 2009
Additional Notes: The author was supported by the Research Council of Norway through Storforsk project “Homological and geometric methods in algebra”, and also by the grant GAČR 201/05/H005 and the research project MSM 0021620839.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.