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Let R be a finite commutative ring with unity. Prove that every non-zero element of R is either a zero-divisor or a unit. What happens if we drop the "finite" condition on R ?

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marked as duplicate by dfeuer, tomasz, Old John, Namaste, mrf Dec 6 '13 at 22:07

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    $\begingroup$ For the infinite case: Look at $\mathbb Z$, what are its zero divisors? Its units? $\endgroup$ – martini Dec 6 '13 at 21:32
  • $\begingroup$ I don't understand why this question have 3 votes down? +1 $\endgroup$ – Valerin Dec 6 '13 at 21:38
  • $\begingroup$ Guys, look at the user's history. Pretty much we are doing the OPs homework... $\endgroup$ – LASV Dec 6 '13 at 21:39
  • $\begingroup$ @LuisValerin: See Luis's comment. $\endgroup$ – tomasz Dec 6 '13 at 21:40
  • $\begingroup$ Is true you are right. $\endgroup$ – Valerin Dec 6 '13 at 21:43