Wikipedia language
In algebraic geometry, a regular scheme is a locally Noetherian scheme whose local rings are regular everywhere. Every smooth scheme is regular, and every regular scheme of finite type over a perfect field is smooth.
For an example of a regular scheme that is not smooth, see Geometrically regular ring § Examples.
Commutative algebraBranch of algebra that studies commutative rings
Regular local ringType of ring in commutative algebra
Noetherian schemeConcept in algebraic geometry
Cohen–Macaulay ringType of commutative ring in mathematicsText from Wikipedia, CC BY-SA 4.0 · Source article