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It is well-known that a group ring of a finite group is semi-simple, and since profinite-groups are projective limits of finite groups, I am thinking per chance profinite groups still possess some good properties inherited from the finite components. As I have found thus far no reference in the direction, I ask here the question: Is the group ring of a profinite group (necessarily) (semi)-hereditary?
Thanks in advance.

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The group ring over what field (or ring)? –  Alex B. Dec 9 '12 at 20:03
    
Basically over the ring of integers. Thanks for the attention. –  awllower Dec 9 '12 at 20:23
    
The group ring of a finite group over the integers is not semi-simple. Indeed, any module $M$ has proper submodules $nM$ for any $n\in \mathbb{N}$. So there are no simple modules. –  Alex B. Dec 9 '12 at 20:36
    
I know that at least it is semi-simple over $C$. So let us suppose that it is semi-simple over some field $k$, and then ask if the profinite group is (semi)-heriditary? –  awllower Dec 11 '12 at 13:32

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