Regular local ring

Symbol-free definition
A local commutative unital ring is said to be regular if its unique maximal ideal is generated (as a module over the ring) by as many elements as the Krull dimension of the ring.

Stronger properties

 * Discrete valuation ring

Weaker properties

 * Local Cohen-Macaulay ring
 * Local domain
 * Unique factorization domain
 * Integral domain: