Burchnall-Chaundy annihilating polynomials for commuting elements in Ore extension rings
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2440756
- author
- Richter, Johan LU and Silvestrov, Sergei LU
- organization
- publishing date
- 2012
- 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
- additional info
- Paper presented at the 6th Baltic-Nordic Workshop Algebra, Geometry, and Mathematical Physics 2010, AGMP-6;Tjärno; 25-31 October 2010
- id
- 76831cdc-0bae-47fe-a0b3-50c4936d8e9c (old id 2440756)
- date added to LUP
- 2016-04-01 10:41:17
- date last changed
- 2022-01-26 01:30:19
@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}}, keywords = {{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}}, doi = {{10.1088/1742-6596/346/1/012021}}, volume = {{346}}, year = {{2012}}, }