Richter, Johan; Silvestrov, Sergei **(2012)**. Burchnall-Chaundy annihilating polynomials for commuting elements in Ore extension rings.* Journal of Physics, Conference Series, 346,*

Download:

Authors:

Richter, Johan
;
Silvestrov, Sergei

Department:

Mathematics (Faculty of Engineering)

Non-commutative Geometry-lup-obsolete

Algebra

Non-commutative Geometry-lup-obsolete

Algebra

Research Group:

Non-commutative Geometry-lup-obsolete

Algebra

Algebra

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.

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.

Keywords:

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

ISSN:

1742-6596

LUP-ID:

76831cdc-0bae-47fe-a0b3-50c4936d8e9c | Link: https://lup.lub.lu.se/record/76831cdc-0bae-47fe-a0b3-50c4936d8e9c
| Statistics