What is an example of integral domain that is not a division ring?
Integral domain that is not a division ring
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$\begingroup$
abstract-algebra
ring-theory
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0@Lmn6 Not a well posed question. – 2011-09-30
3 Answers
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What is the first ring that pops into your head when you think of a ring? Is it a division ring? No! Is it an integral domain? Yes!
Methinks you just need to learn your definitions...
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Hint: think about the word integral
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0@Chris: was that intended for me or Swlabr? If for Swlabr, using $\mathrm{@Swlabr}$ notifies Swlabr. – 2011-09-30
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In a division ring every non zero element is a unit. The only units in $\mathbb{Z}$ are $1$ and $-1$, so $\mathbb{Z}$ is not a division ring but an integral domain.