Integral domain

From Citizendium
Jump to navigation Jump to search
This article is a stub and thus not approved.
Main Article
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
This editable Main Article is under development and subject to a disclaimer.

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]


  • 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.


  1. Serge Lang (1993). Algebra, 3rd ed.. Addison-Wesley, 91-92. ISBN 0-201-55540-9.