The structure of F-pure rings

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The structure of F-pure rings

Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/10605

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Title: The structure of F-pure rings
Author: Aberbach, Ian M.; Enescu, Florian
Keywords: Frobenius splitting ratios
Date: 2003-10-15
Abstract: For a reduced F-finite ring R of characteristic p >0 and q=p^e one can write R^{1/q} = R^{a_q} \oplus M_q, 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 P(R) of R, called the splitting prime, that has the property that R/P(R) is strongly F-regular. We show that this ideal captures significant information with regard to the F-purity of R.
URI: http://hdl.handle.net/10355/10605

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  • Mathematics publications (MU) [119]
    The items in this collection are the scholarly output of the faculty, staff, and students of the Department of Mathematics.

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