在环论中，商环（或称剩余类环）是环对一个理想的商结构。

设为一环，为一双边理想。定义下述等价关系

令为其等价类的集合，其中的元素记作，其中是该元素在上任一代表元。我们可以在上定义环结构：

以上运算是明确定义的（在第二式中须用到是双边理想）。集合配合上述运算称作对的商环。根据定义，商映射是满的环同态，为此同态的核。

如果含单比特，则是的单比特。

注：若条件弱化为是左（或右）理想，上述两式仍可赋予集合左（或右）-模结构。

In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite similar to the quotient groups of group theory and the quotient spaces of linear algebra. One starts with a ring R and a two-sided ideal I in R, and constructs a new ring, the quotient ring R/I, whose elements are the cosets of I in R subject to special + and ⋅ operations.