The main goal of this thesis is to present the theory of Locally Nilpotent Derivations
and to show how it can be used to investigate the structure of the polynomial ring
in two variables k[X;Y] over a field k of characteristic zero. The thesis gives a com-
plete proof of Rentschler's Theorem, which describes all locally nilpotent derivations
of k[X;Y]. Then we present Rentschler's proof of Jung's Theorem, which partially
describes the group of automorphisms of k[X;Y]. Finally, we present the proof of the
Structure Theorem for the group of automorphisms of k[X;Y].
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/35906 |
| Date | January 2017 |
| Creators | Nyobe Likeng, Samuel Aristide |
| Contributors | Daigle, Daniel |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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