May 28th, 2014, 11:23 AM  #1 
Newbie Joined: May 2014 From: Brandon, MS Posts: 2 Thanks: 0  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 nonunit has a unique factorization. I know an integral domain is a ring whose nonzero elements are nonzero divisors. Help! 
May 28th, 2014, 12:11 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
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.)

May 28th, 2014, 01:28 PM  #3 
Senior Member Joined: Nov 2010 From: Berkeley, CA Posts: 174 Thanks: 35 Math Focus: Elementary Number Theory, Algebraic NT, Analytic NT 
But 1+1 is not necessarily equal to 0, so {0,1} may not be closed under addition.

May 28th, 2014, 02:13 PM  #4 
Senior Member Joined: Mar 2012 Posts: 294 Thanks: 88 
Hint: there is an obvious one you have known since childhood.


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domain, factorial, field 
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