Let R be an integral domain. Which of the following statement is not true about R?

Let R be an integral domain. Which of the following statement is not true about R?

Explanation
  • An integral domain is a commutative ring with no zero-divisors, but it does not necessarily have multiplicative inverses for all nonzero elements, so it is not always a division ring.
  • If an integral domain is finite, then it is a field (every nonzero element has a multiplicative inverse).