In mathematics, especially in the area of algebra known as ring theory, an Ore extension, named after Oystein Ore, is a special type of a ring extension whose properties are relatively well understood. Ore extensions appear in several natural contexts, including skew and differential polynomial rings, group algebras of polycyclic groups, enveloping algebras of solvable Lie algebras, and coordinate rings of quantum groups.
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“Where there is reverence there is fear, but there is not reverence everywhere that there is fear, because fear presumably has a wider extension than reverence.”
—Socrates (469–399 B.C.)