##### Wiktionary

**subring**

n. (context algebra English) a ring which is contained in a larger ring, such that the multiplication and addition on the former are a restriction of those on the latter

##### Wikipedia

**Subring**

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.

#### Usage examples of "subring".

Trantor is in the innermost __subring__ of the spiral arms and, believe me, if you could see its night sky, you would think it was in the center of the Galaxy.

Some of the __subrings__ are not quite circular and at least one seems to be braided.