On local orders (Q802713)

Let \(\Lambda\) be a local order in a separable algebra over some local field, such that \({\bar \Lambda}\), the intersection of all maximal overorders, is hereditary. (This latter condition is satisfied if \(\Lambda\) is representation-finite [see \textit{Yu. Drozd}, \textit{V. Kirichenko}, Izv. Akad. Nauk SSSR, Ser. Mat. 37, 715-736 (1973; Zbl 0291.16005)].) The author describes the orders \(\Lambda\) for which every irreducible representation is tame. If \(\Lambda\) is representation- finite, the pullback structure of \(\Lambda\) is exhibited. He observes that representation-finiteness of \(\Lambda\) is tantamount to representation-finiteness of the Bäckström order \(\Lambda +Rad {\bar \Lambda}\).