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 .
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Article
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 .
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integer
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field
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modular arithmetic
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p-adic number
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ring homomorphism
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noncommutative ring
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mathematics
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real number
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ring
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subset
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binary operation
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imaginary unit
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Cambridge University Press
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algebraic structure
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if and only if
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identity element
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