dc.contributor.author | Aberbach, Ian M. | eng |

dc.contributor.author | Enescu, Florian | eng |

dc.date.issued | 2003-10 | eng |

dc.description | This is a preprint of an article published Mathematische Zeitschrift 250 (2005), 791-806. | eng |

dc.description.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. | eng |

dc.identifier.uri | http://hdl.handle.net/10355/10605 | eng |

dc.language | English | eng |

dc.relation.ispartof | Mathematics publications (MU) | eng |

dc.relation.ispartofcommunity | University of Missouri-Columbia. College of Arts and Sciences. Department of Mathematics | eng |

dc.rights | OpenAccess. | eng |

dc.rights.license | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License. | eng |

dc.source.uri | http://www.math.missouri.edu/~aberbach/preprints/index.html | eng |

dc.subject | Frobenius splitting ratios | eng |

dc.subject.lcsh | Gorenstein rings | eng |

dc.subject.lcsh | Cohen-Macaulay rings | eng |

dc.title | The structure of F-pure rings | eng |

dc.type | Article | eng |