Describing Finite Codimensional Polynomial Subalgebras Using Partial Derivatives
(2022) In Master's Theses in Mathematical Sciences FMAM05 20221Mathematics (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. In the referenced paper, the authors present how univariate subalgebras can be described by conditions based on evaluations in certain scalars, and proceed to develop a large theoretical framework to understand the nature of such conditions. The purpose of this thesis is to generalize as many of their results as possible to the multivariate setting K[x]. We include generalized deﬁnitions of the type, spectrum, clusters, αderivations, and α, βevaluation subtractions. We also state and prove generalizations of most of the theorems relating to the spectrum, clusters, αderivation... (More)
 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. In the referenced paper, the authors present how univariate subalgebras can be described by conditions based on evaluations in certain scalars, and proceed to develop a large theoretical framework to understand the nature of such conditions. The purpose of this thesis is to generalize as many of their results as possible to the multivariate setting K[x]. We include generalized deﬁnitions of the type, spectrum, clusters, αderivations, and α, βevaluation subtractions. We also state and prove generalizations of most of the theorems relating to the spectrum, clusters, αderivation spaces, as well as the Main Theorem. We also give a couple of new results pertaining to how αderivation spaces behave when we apply subalgebra conditions on clusters not containing α. (Less)
 Popular Abstract
 Mathematicians like to study different kinds of structures, and this thesis is concerned with one structure in particular, Polynomial Algebras. The main purpose of the thesis is to develop a new method for describing such algebras; by using of conditions.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/9093857
 author
 Leffler, Erik ^{LU}
 supervisor

 Anna Torstensson ^{LU}
 organization
 course
 FMAM05 20221
 year
 2022
 type
 H2  Master's Degree (Two Years)
 subject
 keywords
 Algebra Polynomial Derivations alphaDerivations SAGBI Basis
 publication/series
 Master's Theses in Mathematical Sciences
 report number
 LUTFMA34842022
 ISSN
 14046342
 other publication id
 2022:E42
 language
 English
 id
 9093857
 date added to LUP
 20220815 13:00:33
 date last changed
 20220815 13:00:33
@misc{9093857, 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. In the referenced paper, the authors present how univariate subalgebras can be described by conditions based on evaluations in certain scalars, and proceed to develop a large theoretical framework to understand the nature of such conditions. The purpose of this thesis is to generalize as many of their results as possible to the multivariate setting K[x]. We include generalized deﬁnitions of the type, spectrum, clusters, αderivations, and α, βevaluation subtractions. We also state and prove generalizations of most of the theorems relating to the spectrum, clusters, αderivation spaces, as well as the Main Theorem. We also give a couple of new results pertaining to how αderivation spaces behave when we apply subalgebra conditions on clusters not containing α.}}, author = {{Leffler, Erik}}, issn = {{14046342}}, language = {{eng}}, note = {{Student Paper}}, series = {{Master's Theses in Mathematical Sciences}}, title = {{Describing Finite Codimensional Polynomial Subalgebras Using Partial Derivatives}}, year = {{2022}}, }