Abstract
For a Noetherian local domain R let R + be the absolute integral closure of R and let R ∞ be the perfect closure of R, when R has prime characteristic. In this paper we investigate the projective dimension of residue rings of certain ideals of R + and R ∞. In particular, we show that any prime ideal of R ∞ has a bounded free resolution of countably generated free R ∞-modules. Also, we show that the analogue of this result is true for the maximal ideals of R +, when R has residue prime characteristic. We compute global dimensions of R + and R ∞ in some cases. Some applications of these results are given.
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