SUBRING

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 contains the multiplicative identity of 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 . The latter gives a strictly weaker condition, even for rings that do have a multiplicative identity, so that for instance all ideals become subrings . With definition requiring a multiplicative identity, the only ideal of R ...

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subring

Noun

  1. 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


The above text is a snippet from Wiktionary: subring
and as such is available under the Creative Commons Attribution/Share-Alike License.

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