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dc.contributor.authorAllsop, Nicholas Frederick
dc.date.accessioned2011-02-13T22:30:46Z
dc.date.availableNO_RESTRICTIONen_US
dc.date.available2011-02-13T22:30:46Z
dc.date.issued2000
dc.identifier.urihttp://hdl.handle.net/10179/2132
dc.description.abstractThis dissertation examines the finiteness of the algebraic invariants nA(M) and θA(M). These invariants, based on the ratio of length and multiplicity and the ratio of Loewy length and multiplicity respectively, are studied in general and under certain conditions. The finiteness of θA(M) is established for a large class of algebraic structures. nA(M) is shown to be finite in the low dimensional case as well as when we restrict our attention to special sets of ideals. Also considered in this dissertation are equivalent conditions for the local case to be bounded by the graded case when evaluating nA(M).en_US
dc.language.isoenen_US
dc.publisherMassey Universityen_US
dc.rightsThe Authoren_US
dc.subjectAlgebraen_US
dc.subjectLoewy lengthen_US
dc.subject.otherFields of Research::230000 Mathematical Sciences::230100 Mathematics::230103 Rings and algebrasen_US
dc.titleThe quotient between length and multiplicity : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey Universityen_US
dc.typeThesisen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorMassey Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophy (Ph.D.)en_US


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