On local weak crossed product orders

Th. Theohari-Apostolidi¹ ; A. Tompoulidou¹

¹ School of Mathematics Aristotle University of Thessaloniki Thessaloniki 54124, Greece

Colloquium Mathematicum, Tome 135 (2014) no. 1, pp. 53-68.

Résumé

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 $L/K$.

Détail

DOI : 10.4064/cm135-1-4

Keywords: varlambda alpha local weak crossed product order crossed product algebra alpha integral cocycle sigma operatorname gal mid alpha sigma sigma * inertial group alpha * group units condition first ramification group subgroup moreover describe jacobson radical varlambda without restriction ramification