在数学中，主理想环是使得每个理想均可由单个元素生成的环。

如果一个主理想环同时也是整环，则称之主理想整环（常简写为 PID）。

In mathematics, a principal right (left) ideal ring is a ring R in which every right (left) ideal is of the form xR (Rx) for some element x of R. (The right and left ideals of this form, generated by one element, are called principal ideals.) When this is satisfied for both left and right ideals, such as the case when R is a commutative ring, R can be called a principal ideal ring, or simply principal ring.