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A group ring $R[G]$ is a ring constructed in a natural way from a ring $R$ and a group $G$.

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Do the homological dimension and cohomological dimension for a group agree?

The cohomological and homological dimension of a group do not agree in general. For example, the homological dimension of the group $Z[\frac{1}{2}]$ is one, while its cohomological dimension is 2. Ho …
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