Prove that every finite domain contains an identity element
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Prove that every finite domain contains an identity element.
Please give me help
ring-theory
asked 2012-03-09
user id:26587
23
33bronze badges
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Consider $a$, $a^2$, $a^3$, and so on. By finiteness, there exist natural numbers $m such that $a^m=a^n$. – 2012-03-09
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What exactly do you mean by domain? It sounds like you are asking how to show that every finite integral domain is a field, is that maybe what you wanted to say? If so, this is just Wedderburn's little theorem. – 2012-03-09
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Please don't replace titles with nonsense. If you meant "field" instead of domain, then fields, **by definition** have both a multiplicative and an additive identity, whether they be finite or infinite. – 2012-03-09
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@jay: I assume the question is to show that a finite ring (not necessarily with a unit) which has no zero divisors must in fact have a unit. – 2012-03-09