理想（Ideal）是一个抽象代数中的概念。

环(R,+,·)，已知(R, +)是阿贝尔群。R的子集I称为R的一个右理想，若I满足：

类似地，I称为R的左理想，若以下条件成立：

若I既是R的右理想，也是R的左理想，则称I为R的双边理想，简称R上的理想。

In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring. Ideals generalize certain subsets of the integers, such as the even numbers or the multiples of 3. Addition and subtraction of even numbers preserves evenness, and multiplying an even number by any other integer results in another even number; these closure and absorption properties are the defining properties of an ideal. An ideal can be used to construct a quotient ring similarly to the way that, in group theory, a normal subgroup can be used to construct a quotient group.