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Locally Nilpotent Derivations and Their Quasi-Extensions

In this thesis, we introduce the theory of locally nilpotent derivations and use it to compute certain ring invariants.
We prove some results about quasi-extensions of derivations and use them to show that certain rings are non-rigid.
Our main result states that if k is a field of characteristic zero, C is an affine k-domain and
B = C[T,Y] / < T^nY - f(T) >, where n >= 2 and f(T) \in C[T] is such that
delta^2(f(0)) != 0 for all nonzero locally nilpotent derivations delta of C,
then ML(B) != k.
This shows in particular that the ring B is not a polynomial ring over k.

Identiferoai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/35072
Date January 2016
CreatorsChitayat, Michael
ContributorsDaigle, Daniel
PublisherUniversité d'Ottawa / University of Ottawa
Source SetsUniversité d’Ottawa
LanguageEnglish
Detected LanguageEnglish
TypeThesis

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