Telescope conjecture, idempotent ideals, and the transfinite radical

Details Telescope conjecture, idempotent ideals, and the transfinite radical Telescope conjecture, idempotent ideals, and the transfinite radical

2008-02-15

arxiv.org/abs/0802.2189v2

Trans. Amer. Math. Soc. 362 (2010), 1475-1489

Mathematics

Representation Theory

14 pages, a comment on the Krull-Gabriel dimension added to section 4

Scientific paper

10.1090/s0002-9947-09-04812-0

We show that for an artin algebra $\Lambda$, the telescope conjecture for module categories is equivalent to certain idempotent ideals of 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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