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.author | Smith, Thomasin Ann | |
| dc.date.accessioned | 2017-11-05T19:05:48Z | |
| dc.date.available | 2017-11-05T19:05:48Z | |
| dc.date.issued | 1996 | |
| dc.description.abstract | In 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.uri | http://hdl.handle.net/10179/12224 | |
| dc.language.iso | en | en_US |
| dc.publisher | Massey University | en_US |
| dc.rights | The Author | en_US |
| dc.subject | Rings (Algebra) | en_US |
| dc.subject | Ideals (Algebra) | en_US |
| dc.title | 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 | en_US |
| dc.type | Thesis | en_US |
| massey.contributor.author | Smith, Thomasin Ann | |
| thesis.degree.discipline | Mathematics | en_US |
| thesis.degree.grantor | Massey University | en_US |
| thesis.degree.level | Masters | en_US |
| thesis.degree.name | Master of Science (M. Sc.) | en_US |
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