On arithmetical associated orders
Let \(p\) be an odd prime, and \(L/K\) a totally ramified finite abelian extension of \(p\)-adic fields with Galois group \(G\). For each ideal \(I\) of the valuation ring of \(L\), the associated order \(\text{End}_{\mathbb{Q}_p [G]}(I)\) is an interesting invariant of the \(\mathbb{Z}_p [G]\)-structure of \(I\). The authors show that, unless \(G\) is cyclic, no such order can contain any idempotent of \(\mathbb{Q}_p [G]\) which does not already lie in \(\mathbb{Z}_p[G]\). This puts a strong restriction on the possible structures of these orders. An algorithm for computing associated orders is also described, and explicit examples are computed.
totally ramified finite abelian extension of \(p\)-adic fields
scientific article; zbMATH DE number 894612