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Locally Nilpotent Derivations and Their Quasi-ExtensionsChitayat, Michael January 2016 (has links)
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.
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Locally Nilpotent Derivations on Polynomial Rings in Two Variables over a Field of Characteristic Zero.Nyobe Likeng, Samuel Aristide January 2017 (has links)
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].
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