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ISSN 1088-6850(e) ISSN 0002-9947(p)

Telescope conjecture, idempotent ideals, and the transfinite radical

Author(s): Jan Stovícek
Journal: Trans. Amer. Math. Soc. 362 (2010), 1475-1489.
MSC (2000): Primary 18E35; Secondary 16E30, 16G60
Posted: October 9, 2009
MathSciNet review: 2563737
Retrieve article in: PDF

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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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