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Burchnall-Chaundy annihilating polynomials for commuting elements in Ore extension rings

Richter, Johan LU and Silvestrov, Sergei LU (2012) In Journal of Physics, Conference Series 346.
Abstract
In this article further progress is made in extending the Burchnall-Chaundy type determinant construction of annihilating polynomial for commuting elements to broader classes of rings and algebras by deducing an explicit general formula for the coefficients of the annihilating polynomial obtained by the Burchnall-Chaundy type determinant construction in Ore extension rings. It is also demonstrated how this formula can be used to compute the annihilating polynomials in several examples of commuting elements in Ore extensions. Also it is demonstrated that additional properties which may be possessed by the endomorphism, such as for example injectivity, may influence strongly the annihilating polynomial.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
annihilating polynomial, algebraic dependence, Burchnall-Chaundy determinant construction, commuting elements, Ore extensions
in
Journal of Physics, Conference Series
volume
346
publisher
IOP Publishing
external identifiers
  • wos:000305176100021
  • scopus:84858195933
ISSN
1742-6596
DOI
10.1088/1742-6596/346/1/012021
language
English
LU publication?
yes
id
76831cdc-0bae-47fe-a0b3-50c4936d8e9c (old id 2440756)
date added to LUP
2012-08-31 16:24:01
date last changed
2017-03-26 03:15:27
@article{76831cdc-0bae-47fe-a0b3-50c4936d8e9c,
  abstract     = {In this article further progress is made in extending the Burchnall-Chaundy type determinant construction of annihilating polynomial for commuting elements to broader classes of rings and algebras by deducing an explicit general formula for the coefficients of the annihilating polynomial obtained by the Burchnall-Chaundy type determinant construction in Ore extension rings. It is also demonstrated how this formula can be used to compute the annihilating polynomials in several examples of commuting elements in Ore extensions. Also it is demonstrated that additional properties which may be possessed by the endomorphism, such as for example injectivity, may influence strongly the annihilating polynomial.},
  author       = {Richter, Johan and Silvestrov, Sergei},
  issn         = {1742-6596},
  keyword      = {annihilating polynomial,algebraic dependence,Burchnall-Chaundy determinant construction,commuting elements,Ore extensions},
  language     = {eng},
  publisher    = {IOP Publishing},
  series       = {Journal of Physics, Conference Series},
  title        = {Burchnall-Chaundy annihilating polynomials for commuting elements in Ore extension rings},
  url          = {http://dx.doi.org/10.1088/1742-6596/346/1/012021},
  volume       = {346},
  year         = {2012},
}