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

Research output: Contribution to journalArticle

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.

Details

Authors
  • Johan Richter
  • Sergei Silvestrov
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • annihilating polynomial, algebraic dependence, Burchnall-Chaundy determinant construction, commuting elements, Ore extensions
Original languageEnglish
JournalJournal of Physics, Conference Series
Volume346
Publication statusPublished - 2012
Publication categoryResearch
Peer-reviewedYes

Bibliographic note

Paper presented at the 6th Baltic-Nordic Workshop Algebra, Geometry, and Mathematical Physics 2010, AGMP-6;Tjärno; 25-31 October 2010