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dc.contributor.authorAberbach, Ian M.eng
dc.contributor.authorEnescu, Florianeng
dc.date.issued2003-10eng
dc.descriptionThis is a preprint of an article published Mathematische Zeitschrift 250 (2005), 791-806.eng
dc.description.abstractFor 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.urihttp://hdl.handle.net/10355/10605eng
dc.languageEnglisheng
dc.relation.ispartofMathematics publications (MU)eng
dc.relation.ispartofcommunityUniversity of Missouri-Columbia. College of Arts and Sciences. Department of Mathematicseng
dc.rightsOpenAccess.eng
dc.rights.licenseThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.eng
dc.source.urihttp://www.math.missouri.edu/~aberbach/preprints/index.htmleng
dc.subjectFrobenius splitting ratioseng
dc.subject.lcshGorenstein ringseng
dc.subject.lcshCohen-Macaulay ringseng
dc.titleThe structure of F-pure ringseng
dc.typeArticleeng


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