Derivations in Univariate Polynomial Subalgebras of Finite Codimension
(2021) In Bachelor's Theses in Mathematical Sciences FMAL01 20211Mathematics (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:
http://lup.lub.lu.se/student-papers/record/9067084
- author
- Leffler, Erik LU
- supervisor
- organization
- course
- FMAL01 20211
- year
- 2021
- 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}}, }