regular local ring

In commutative algebra, a regular local ring is a Noetherian local ring having the property that the minimal number of generators of its maximal ideal is equal to its Krull dimension. In symbols, let A be a Noetherian local ring with maximal ideal m, and suppose a₁, ..., a_n is a minimal set of generators of m. Then by Krull's principal ideal theorem n = dim A, and A is defined to be regular if n = dim A.