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Sticky Note
Let R be an integral domain. Which of the following statement is not true about R?
  1. R is division ring
  2. If R is finite, then it is a field
  3. R has no zero-divisor
  4. None of these
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).

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