Length functions determined by killing powers of several ideals in a local ring

 dc.contributor.author Fields, J. Bruce dc.contributor.advisor Hochester, Melvin dc.date.accessioned 2007-11-07T19:37:15Z dc.date.available NO_RESTRICTION en_US dc.date.available 2007-11-07T19:37:15Z dc.date.issued 2000 dc.date.submitted 2000 dc.identifier.uri https://hdl.handle.net/2027.42/57281 dc.description.abstract Given a local ring R and n ideals whose sum is primary to the maximal ideal of R, one may define a function which takes an n-tuple of exponents to the length of the quotient of R by sum of the ideals raised to the respective exponents. This quotient can also be obtained by taking the tensor product of the quotients of R by the various powers of the ideals. This thesis studies these functions as well as the functions obtained by replacing the tensor product by a higher Tor. These functions are shown to have rational generating functions under certain conditions. en_US dc.format.extent 372234 bytes dc.format.mimetype application/pdf dc.language.iso en_US en_US dc.subject Commutative Algebra en_US dc.subject Rings en_US dc.subject Hilbert Functions en_US dc.subject Hilbert-Kunz Functions en_US dc.subject Intersection Multiplicities en_US dc.subject Quasipolynomial Functions en_US dc.subject.other Mathematics en_US dc.title Length functions determined by killing powers of several ideals in a local ring en_US dc.type Thesis en_US dc.description.thesisdegreename Ph.D. en_US dc.description.thesisdegreediscipline Mathematics en_US dc.description.thesisdegreegrantor University of Michigan en_US dc.contributor.committeemember Barvonik, Alexandre dc.contributor.committeemember Miller, Claudia dc.contributor.committeemember Sklar, Lawrence dc.contributor.committeemember Smith, Karen dc.subject.hlbsecondlevel Mathematics dc.subject.hlbtoplevel Science dc.identifier.uniqname bfields en_US dc.description.bitstreamurl http://deepblue.lib.umich.edu/bitstream/2027.42/57281/1/fields_thesis.pdf en_US dc.owningcollname Dissertations and Theses (Ph.D. and Master's)
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