Telescope conjecture, idempotent ideals, and the transfinite radical

Abstract

We show that for an artin algebra A, the telescope conjecture for module categories is equivalent to certain idempotent ideals of mod-A 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

Keywords

• Telescope
• conjecture
• idempotent
• ideals
• and
• the
• transfinite
• radical