Ore algebra

In computer algebra, an Ore algebra is a special kind of iterated Ore extension that can be used to represent linear functional operators, including linear differential and/or recurrence operators.

[1] The concept is named after Øystein Ore. Let

be a (commutative) field and

be a commutative polynomial ring (with

The iterated skew polynomial ring

σ

δ

σ

δ

is called an Ore algebra when the

commute for

Ore algebras satisfy the Ore condition, and thus can be embedded in a (skew) field of fractions.

The constraint of commutation in the definition makes Ore algebras have a non-commutative generalization theory of Gröbner basis for their left ideals.

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