设(R,+,·)为环，若S是R的一个非空子集，且(S,+,·)也是环，则称(S,+,·)为(R,+,·)的子环（subring）。

设(R,+,·)为环，S是R的一个非空子集。(S,+,·)是(R,+,·)的子环，当且仅当：

或等价地：

也就是说：

如果要求环还包含乘法单比特，那么就要在上述条件加上1∈S这一条。

In mathematics, a subring of R is a subset of a ring that is itself a ring when binary operations of addition and multiplication on R are restricted to the subset, and which shares the same multiplicative identity as R. For those who define rings without requiring the existence of a multiplicative identity, a subring of R is just a subset of R that is a ring for the operations of R (this does imply it contains the additive identity of R). The latter gives a strictly weaker condition, even for rings that do have a multiplicative identity, so that for instance all ideals become subrings (and they may have a multiplicative identity that differs from the one of R). With definition requiring a multiplicative identity (which is used in this article), the only ideal of R that is a subring of R is R itself.