Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4666989 | Advances in Mathematics | 2010 | 17 Pages |
Abstract
Let R be a left and right ℵ0-Noetherian ring. We show that if all projective left and all projective right R-modules have finite injective dimension, then all injective left and all injective right R-modules have finite projective dimension. Using this result, we prove that the invariants and , which were introduced by Gedrich and Gruenberg (1987) [15], , are equal for any group G. As an application of the latter equality, we show that a group G is finite if and only if , where is the generalized cohomological dimension of groups introduced by Ikenaga (1984) [21].
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