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 $L/K$.
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
Affiliations des auteurs :
Th. Theohari-Apostolidi
1
;
A. Tompoulidou
1
1
School of Mathematics Aristotle University of Thessaloniki Thessaloniki 54124, Greece
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author = {Th. Theohari-Apostolidi and A. Tompoulidou},
title = {On local weak crossed product orders},
journal = {Colloquium Mathematicum},
pages = {53--68},
year = {2014},
volume = {135},
number = {1},
doi = {10.4064/cm135-1-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm135-1-4/}
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AU - A. Tompoulidou
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Th. Theohari-Apostolidi; A. Tompoulidou. On local weak crossed product orders. Colloquium Mathematicum, Tome 135 (2014) no. 1, pp. 53-68. doi: 10.4064/cm135-1-4
