数学上，偏序集 P 适合升链条件，若任意 P 的元素的升链 a₁ ≤ a₂ ≤ ...最终固定，就是说存在正整数 n，使得对所有 m > n，有 a_m = a_n。 类似地，P 适合降链条件，若任意P的元素的降链 a₁ ≥ a₂ ≥ ...最终固定 （就是说不存在无穷降链）。

P 的升链条件等价于最大条件：所有 P 的非空子集都有极大元。类似地，降链条件等价于最小条件：所有 P 的非空子集都有极小元。

In mathematics, the ascending chain condition (ACC) and descending chain condition (DCC) are finiteness properties satisfied by some algebraic structures, most importantly, ideals in certain commutative rings. These conditions played an important role in the development of the structure theory of commutative rings in the works of David Hilbert, Emmy Noether, and Emil Artin. The conditions themselves can be stated in an abstract form, so that they make sense for any partially ordered set. This point of view is useful in abstract algebraic dimension theory due to Gabriel and Rentschler.