Algebraic Properties of Ore Extensions and Their Commutative Subrings
(2014) Abstract
 This thesis deals with a class of rings known as Ore extensions. An Ore extension can be described as a noncommutative ring of polynomials in one variable.
A special focus of the thesis is the study of commuting elements in Ore extensions. In the first two papers in the thesis we prove that commuting elements of Ore extensions are in many cases algebraically dependent. In doing this we extend a classical result for the ordinary ring of polynomials. We also show how to compute the polynomial that annihilates a pair of commuting elements by a construction that generalizes the classical resultant.
In the third paper we deal with the simplicity of Ore extension, and give a number of necessary and... (More)  This thesis deals with a class of rings known as Ore extensions. An Ore extension can be described as a noncommutative ring of polynomials in one variable.
A special focus of the thesis is the study of commuting elements in Ore extensions. In the first two papers in the thesis we prove that commuting elements of Ore extensions are in many cases algebraically dependent. In doing this we extend a classical result for the ordinary ring of polynomials. We also show how to compute the polynomial that annihilates a pair of commuting elements by a construction that generalizes the classical resultant.
In the third paper we deal with the simplicity of Ore extension, and give a number of necessary and sufficient conditions. The fourth and sixth paper return to the study of commuting elements and show that the centralizer of an element of an Ore extension is commutative in certain cases, as well as various other properties. In the fifth paper we show that the construction of Ore extensions really gives an associative ring. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4616248
 author
 Richter, Johan ^{LU}
 supervisor

 Sergei Silvestrov ^{LU}
 opponent

 Professor Abramov, Viktor, University of Tartu, Estonia
 organization
 publishing date
 2014
 type
 Thesis
 publication status
 published
 subject
 keywords
 Ore extension, Noncommutative algebra, Algebraic dependence
 defense location
 Lecture hall MH:C, Centre for Mathematical Sciences, SÃ¶lvegatan 18, Lund University Faculty of Engineering
 defense date
 20140929 13:15:00
 ISBN
 9789176230688
 language
 English
 LU publication?
 yes
 id
 7cf9195d468f469297d4872f62af32c7 (old id 4616248)
 date added to LUP
 20160404 12:56:27
 date last changed
 20181121 21:11:27
@phdthesis{7cf9195d468f469297d4872f62af32c7, abstract = {{This thesis deals with a class of rings known as Ore extensions. An Ore extension can be described as a noncommutative ring of polynomials in one variable. <br/><br> <br/><br> A special focus of the thesis is the study of commuting elements in Ore extensions. In the first two papers in the thesis we prove that commuting elements of Ore extensions are in many cases algebraically dependent. In doing this we extend a classical result for the ordinary ring of polynomials. We also show how to compute the polynomial that annihilates a pair of commuting elements by a construction that generalizes the classical resultant.<br/><br> <br/><br> In the third paper we deal with the simplicity of Ore extension, and give a number of necessary and sufficient conditions. The fourth and sixth paper return to the study of commuting elements and show that the centralizer of an element of an Ore extension is commutative in certain cases, as well as various other properties. In the fifth paper we show that the construction of Ore extensions really gives an associative ring.}}, author = {{Richter, Johan}}, isbn = {{9789176230688}}, keywords = {{Ore extension; Noncommutative algebra; Algebraic dependence}}, language = {{eng}}, school = {{Lund University}}, title = {{Algebraic Properties of Ore Extensions and Their Commutative Subrings}}, url = {{https://lup.lub.lu.se/search/files/6024038/4616258.pdf}}, year = {{2014}}, }