Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 18E35, 16E30, 16G60

Retrieve articles in all journals with MSC (2000): 18E35, 16E30, 16G60

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

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.

American Mathematical Society