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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