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University of Ottawa

1.
Chitayat, Michael.
*Locally**Nilpotent* Derivations and Their Quasi-Extensions
.

Degree: 2016, University of Ottawa

URL: http://hdl.handle.net/10393/35072

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) ∈ 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.

Subjects/Keywords: Locally Nilpotent Derivation; Commutative Algebra

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Chitayat, M. (2016). Locally Nilpotent Derivations and Their Quasi-Extensions . (Thesis). University of Ottawa. Retrieved from http://hdl.handle.net/10393/35072

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Chitayat, Michael. “Locally Nilpotent Derivations and Their Quasi-Extensions .” 2016. Thesis, University of Ottawa. Accessed July 07, 2020. http://hdl.handle.net/10393/35072.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Chitayat, Michael. “Locally Nilpotent Derivations and Their Quasi-Extensions .” 2016. Web. 07 Jul 2020.

Vancouver:

Chitayat M. Locally Nilpotent Derivations and Their Quasi-Extensions . [Internet] [Thesis]. University of Ottawa; 2016. [cited 2020 Jul 07]. Available from: http://hdl.handle.net/10393/35072.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Chitayat M. Locally Nilpotent Derivations and Their Quasi-Extensions . [Thesis]. University of Ottawa; 2016. Available from: http://hdl.handle.net/10393/35072

Not specified: Masters Thesis or Doctoral Dissertation

2.
Nyobe Likeng, Samuel Aristide.
*Locally**Nilpotent* Derivations on Polynomial Rings in Two Variables over a Field of Characteristic Zero.

Degree: 2017, University of Ottawa

URL: http://hdl.handle.net/10393/35906

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].

Subjects/Keywords: Locally Nilpotent Derivation; Rentschler's Theorem; Tame Automorphisms; Wild Automorphisms

…charac-
be a *locally* *nilpotent* *derivation*. Then
α
of
B
and a polynomial
f (X)… …Jung's Theorem in this thesis.
3
Let us discuss *locally* *nilpotent* derivations in… …the set of *locally* *nilpotent* derivations of a
B.
It was known before Rentschler's… …article that *locally* *nilpotent* derivations are
More precisely, if
X ⊆ Cn
is its ane coordinate… …algebraic variety X .
the *locally* *nilpotent* derivations of
Ga
on the algebraic variety
2
C
X…

Record Details Similar Records

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Nyobe Likeng, S. A. (2017). Locally Nilpotent Derivations on Polynomial Rings in Two Variables over a Field of Characteristic Zero. (Thesis). University of Ottawa. Retrieved from http://hdl.handle.net/10393/35906

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Nyobe Likeng, Samuel Aristide. “Locally Nilpotent Derivations on Polynomial Rings in Two Variables over a Field of Characteristic Zero. ” 2017. Thesis, University of Ottawa. Accessed July 07, 2020. http://hdl.handle.net/10393/35906.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Nyobe Likeng, Samuel Aristide. “Locally Nilpotent Derivations on Polynomial Rings in Two Variables over a Field of Characteristic Zero. ” 2017. Web. 07 Jul 2020.

Vancouver:

Nyobe Likeng SA. Locally Nilpotent Derivations on Polynomial Rings in Two Variables over a Field of Characteristic Zero. [Internet] [Thesis]. University of Ottawa; 2017. [cited 2020 Jul 07]. Available from: http://hdl.handle.net/10393/35906.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Nyobe Likeng SA. Locally Nilpotent Derivations on Polynomial Rings in Two Variables over a Field of Characteristic Zero. [Thesis]. University of Ottawa; 2017. Available from: http://hdl.handle.net/10393/35906

Not specified: Masters Thesis or Doctoral Dissertation