On local weak crossed product orders
Volume 135 / 2014
Colloquium Mathematicum 135 (2014), 53-68
MSC: Primary 16S35, 16H10, 16G30, 11S23.
DOI: 10.4064/cm135-1-4
Abstract
Let $\varLambda =(S/R,\alpha )$ be a local weak crossed product order in the crossed product algebra $A=(L/K,\alpha )$ with integral cocycle, and $H=\{\sigma \in \operatorname{Gal} (L/K)\mid \alpha (\sigma ,\sigma ^{-1})\in S^{*}\}$ the inertial group of $\alpha $, for $S^{*}$ the group of units of $S$. We give a condition for the first ramification group of $L/K$ to be a subgroup of $H$. Moreover we describe the Jacobson radical of $\varLambda $ without restriction on the ramification of $L/K$.
