In this paper, we show that the injective dimension of all projective modules over a countable ring is bounded by the self-injective dimension of the ring. We also examine the extent to which the flat length of all injective modules is bounded by the flat length of an injective cogenerator. To that end, we study the relation between these finiteness conditions on the ring and certain properties of the (strict) Mittag-Le?er modules. We also examine the relation between the self-injective dimension of the integral group ring of a group and Ikenaga's generalized (co-)homological dimension.
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