I'm not sure if I understand this question.

An integral domain is a commutative ring (with unity) without zero-divisors. The question ask for an integral domain that is not an integral domain?

Can someone shed some understanding?

Thanks in advance

  • 1
    $\begingroup$ maybe they mean without $1$? $\endgroup$ – peter a g May 11 '16 at 11:12
  • 1
    $\begingroup$ Note that an integral domain is (as part of the definition) not the zero-ring. $\endgroup$ – Tobias Kildetoft May 11 '16 at 11:12
  • $\begingroup$ It would have been stated if they had wanted 1. $\endgroup$ – Mathematicing May 11 '16 at 11:12
  • $\begingroup$ For future reference please make the body of the Question self-contained with respect to stating the problem, not relying on the title alone to carry this burden. $\endgroup$ – hardmath May 11 '16 at 11:19

Essentially, you want a commutative ring without zero-divisors and without unity. So take $2\Bbb Z$ for instance


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