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Zbl 1151.16021
Bley, Werner; Johnston, Henri
Computing generators of free modules over orders in group algebras. (English)
[J] J. Algebra 320, No. 2, 836-852 (2008). ISSN 0021-8693

Let $E$ be an algebraic number field with maximal order $\cal O$, and let $\Lambda$ be an $\cal O$-order in the group ring $E[G]$ over a finite group $G$. Under the assumption that the Schur indices of all $E$-rational irreducible characters of $G$ are 1, the authors give a computationally useful criterion for $\Lambda$-lattices to be free of a given rank. An application to Galois modules is indicated.
[Wolfgang Rump (Stuttgart)]

MSC 2000:: *16H05 Orders and arithmetic, separable associative algebras
20C05 Group rings of finite groups and their modules (group theory)
16S34 Group rings (assoc. rings)
11R54 Other algebras and orders, and their zeta and L-functions

Keywords: Galois module structure; associated orders; group algebras

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