subring
Sign in to saveIn mathematics, a subring of a ring is a subset of that is itself a ring when binary operations of addition and multiplication on R are restricted to the subset, and that shares the same multiplicative identity as .
~4 min read
Encyclopedic overview
11 sectionsContents
- Definition
- Variations
- Examples
- Subring generated by a set
- Ring extension
- Adjoining
- Prime subring
- See also
- Notes
- References
- General references
In mathematics, a subring of a ring is a subset of that is itself a ring when binary operations of addition and multiplication on R are restricted to the subset, and that shares the same multiplicative identity as .
== Definition == A subring of a ring is a subset of that preserves the structure of the ring, i.e. a ring with . Equivalently, it is both a subgroup of and a submonoid of .
Excerpted from Wikipedia’s “subring” article, available under the CC BY-SA 4.0 licence.