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May 28th, 2014, 11:23 AM   #1
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Question Factorial Domain

I need to find a factorial domain which does not contain a field.

I know a factorial domain is an integral domain where every non-unit has a unique factorization.

I know an integral domain is a ring whose non-zero elements are non-zero divisors.

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May 28th, 2014, 12:11 PM   #2
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What does it mean to contain a field? Surely the set containing only 0 and 1 is a subring and this ring is itself a field. (All domains contain distinct elements 0 and 1.)
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May 28th, 2014, 01:28 PM   #3
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But 1+1 is not necessarily equal to 0, so {0,1} may not be closed under addition.
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May 28th, 2014, 02:13 PM   #4
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Hint: there is an obvious one you have known since childhood.
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