在交换代数中，正则局部环是使得其极大理想的最小生成元个数等于其Krull维度的局部诺特环。

设 为局部诺特环。设 为 的一组最小生成元，一般而言有 。当 时，称 为正则局部环。

根据中山正引理，局部诺特环 为正则局部环若且唯若 。

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.