Abstract
For a reduced F-finite ring R of characteristic p>0 and q=p e one can write Open image in new window where M q has no free direct summands over R. We investigate the structure of F-finite, F-pure rings R by studying how the numbers a q grow with respect to q. This growth is quantified by the splitting dimension and the splitting ratios of R which we study in detail. We also prove the existence of a special prime ideal Open image in new window (R) of R, called the splitting prime, that has the property that R/ Open image in new window (R) is strongly F-regular. We show that this ideal captures significant information with regard to the F-purity of R.
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