# integral domain

## English

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### Noun

integral domain (plural integral domains)

1. (algebra) A commutative ring with identity not equal to zero which has no zero divisors. [1911] [1]
Ring R is an integral domain if and only if the polynomial ring ${\displaystyle R[x]}$ is an integral domain.
For any integral domain there can be derived an associated field of fractions.

### References

1. ^ Jeff Miller, editor (2016) Earliest Known Uses of Some of the Words of Mathematics[1], archived from the original on 17 August 2017