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 understand 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/studentpapers/record/9067084
 author
 Leffler, Erik ^{LU}
 supervisor

 Anna Torstensson ^{LU}
 organization
 course
 FMAL01 20211
 year
 2021
 type
 M2  Bachelor Degree
 subject
 keywords
 Algebra, Polynomials, SAGBIbasis, derivations, alphaderivations, Subalgebra conditions.
 publication/series
 Bachelor's Theses in Mathematical Sciences
 report number
 LUTFMA40072021
 ISSN
 16546229
 other publication id
 2021:K39
 language
 English
 id
 9067084
 date added to LUP
 20220929 16:01:58
 date last changed
 20220929 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 understand 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 = {{16546229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor's Theses in Mathematical Sciences}}, title = {{Derivations in Univariate Polynomial Subalgebras of Finite Codimension}}, year = {{2021}}, }