Abstract
Every module has a minimal pure injective resolution. For a flat modul over a noetherian ring, the structure of the pure injective modules appearing in such a resolution is now known and can be used to give information about minimal pure injective resolutions of flat modules. This information can in turn be used to give new proofs of results about the projective dimension of flat modules and at the same time sharpen these results. A change of ring theorem gives the perhaps surprising result that the pure injective dimensions of the coordinate rings of affine algebraic varieties over some fixed ground field are the same for all varieties of a given dimension n.
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