Abstract.
For a reduced F-finite ring R of characteristic p>0 and q=pe one can write 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 (R) of R, called the splitting prime, that has the property that R/(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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Dedicated to Professor Melvin Hochster on the occasion of his sixtieth birthday
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Aberbach, I., Enescu, F. The structure of F-pure rings. Math. Z. 250, 791–806 (2005). https://doi.org/10.1007/s00209-005-0776-y
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DOI: https://doi.org/10.1007/s00209-005-0776-y