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. The concept is named after Øystein Ore.
Definition
Let be a field and be a commutative polynomial ring. The iterated skew polynomial ring is called an Ore algebra when the and commute for, and satisfy, for.Properties
Ore algebras satisfy the Ore condition, and thus can be embedded in a 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.