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

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Author

  • Johan Richter
  • Sergei Silvestrov

Summary, in English

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.

Publishing year

2012

Language

English

Publication/Series

Journal of Physics: Conference Series

Volume

346

Document type

Journal article

Publisher

IOP Publishing

Topic

  • Mathematics

Keywords

  • annihilating polynomial
  • algebraic dependence
  • Burchnall-Chaundy determinant construction
  • commuting elements
  • Ore extensions

Status

Published

Research group

  • Non-commutative Geometry
  • Algebra

ISBN/ISSN/Other

  • ISSN: 1742-6596