Bounds on the arithmetic degree : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematics at Massey University

dc.contributor.authorSmith, Thomasin Ann
dc.date.accessioned2017-11-05T19:05:48Z
dc.date.available2017-11-05T19:05:48Z
dc.date.issued1996
dc.description.abstractIn this thesis we study the arithmetic degree theory of polynomial ideals. The main objectives are: (i) to show whether we can generalize a lower bound on the arithmetic degree of monomial ideals to the arithmetic degree of arbitrary homogeneous ideals; and (ii) to explain whether some known bounds for the geometric degree can be restated in terms of bounds on the arithmetic degree. We give a negative answer to all questions raised by constructing counterexamples. In some cases we provide a general method for constructing such counterexamples. Concerning properties of the arithmetic degree, we give a new Bezout-type theorem. Finally we take a brief look at open problems concerning the arithmetic degree under hypersurface sections.en_US
dc.identifier.urihttp://hdl.handle.net/10179/12224
dc.language.isoenen_US
dc.publisherMassey Universityen_US
dc.rightsThe Authoren_US
dc.subjectRings (Algebra)en_US
dc.subjectIdeals (Algebra)en_US
dc.titleBounds on the arithmetic degree : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematics at Massey Universityen_US
dc.typeThesisen_US
massey.contributor.authorSmith, Thomasin Ann
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorMassey Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Science (M. Sc.)en_US
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