## Quick Reference

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.