integral domain

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A commutative ring R with identity, with the additional property that

9. For all a and b in R, ab=0 only if a=0 or b=0.(The axiom numbering follows on from that used for ring.) Thus an integral domain is a commutative ring with identity with no divisors of zero. The natural example is the set Z of all integers with the usual addition and multiplication. Any field is an integral domain. Further examples of integral domains (these are not fields) are: the set Z[√2] of all real numbers of the form a+b√2, where a and b are integers, and the set R[x] of all polynomials in an indeterminate x, with real coefficients, each with the normal addition and multiplication.

Subjects: Mathematics.

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