Integral domain

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In ring theory, an integral domain is a commutative ring in which there are no non-trivial zero divisors: that is the product of non-zero elements is again non-zero. The term entire ring is sometimes used.[1]

Properties

  • A commutative ring is an integral domain if and only if the zero ideal is prime.
  • A ring is an integral domain if and only if it is isomorphic to a subring of a field.

References

  1. Serge Lang (1993). Algebra, 3rd ed.. Addison-Wesley, 91-92. ISBN 0-201-55540-9. 
  • Iain T. Adamson (1972). Elementary rings and modules. Oliver and Boyd. ISBN 0-05-002192-3. 
  • David Sharpe (1987). Rings and factorization. Cambridge University Press. ISBN 0-521-33718-6.