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# LUP Student Papers

## LUND UNIVERSITY LIBRARIES

### Derivations in Univariate Polynomial Subalgebras of Finite Codimension

(2021) In Bachelor's Theses in Mathematical Sciences FMAL01 20211
Mathematics (Faculty of Engineering)
Abstract
In this text we continue the work of describing subalgebras of K[x] of finite codimension that was started in “Describing subalgebras of K[x] using derivatives” [2]. In the referenced paper, the authors present how such subalgebras can be described by conditions on the values in certain points and proceed to develop a large theoretical framework to under-stand the nature of such conditions. The authors state and prove a Main Theorem regarding the form that such conditions can exhibit. They also propose a Main Conjecture, a sharpening of the Main Theorem. After having restated the required theory from “Describing subalgebras of K[x] using derivatives” [2], we will present a proof of the Main Conjecture.
Popular Abstract
This text contains a proof of a conjecture that was posed in “Describing subalgebras of K[x] using derivatives” [2]. The theory of the referenced paper revolves around describing certain mathematical structures, namely univariate polynomial algebras, in a novel way. The conjecture that is proved in this paper relates to what these descriptions look like.
Please use this url to cite or link to this publication:
author
supervisor
organization
course
FMAL01 20211
year
type
M2 - Bachelor Degree
subject
keywords
Algebra, Polynomials, SAGBI-basis, derivations, alpha-derivations, Subalgebra conditions.
publication/series
Bachelor's Theses in Mathematical Sciences
report number
LUTFMA-4007-2021
ISSN
1654-6229
other publication id
2021:K39
language
English
id
9067084
date added to LUP
2022-09-29 16:01:58
date last changed
2022-09-29 16:01:58
```@misc{9067084,
abstract     = {{In this text we continue the work of describing subalgebras of K[x] of finite codimension that was started in “Describing subalgebras of K[x] using derivatives” [2]. In the referenced paper, the authors present how such subalgebras can be described by conditions on the values in certain points and proceed to develop a large theoretical framework to under-stand the nature of such conditions. The authors state and prove a Main Theorem regarding the form that such conditions can exhibit. They also propose a Main Conjecture, a sharpening of the Main Theorem. After having restated the required theory from “Describing subalgebras of K[x] using derivatives” [2], we will present a proof of the Main Conjecture.}},
author       = {{Leffler, Erik}},
issn         = {{1654-6229}},
language     = {{eng}},
note         = {{Student Paper}},
series       = {{Bachelor's Theses in Mathematical Sciences}},
title        = {{Derivations in Univariate Polynomial Subalgebras of Finite Codimension}},
year         = {{2021}},
}

```