November 27th, 2007, 01:46 PM  #1 
Newbie Joined: Nov 2007 Posts: 7 Thanks: 0  rings and fields
Let R be a ring, F a subring that is a field. Let w be an element in R that is not in F. Prove that all the elements a + bw with a and b in F are distinct.

December 6th, 2007, 03:49 AM  #2  
Member Joined: Dec 2006 Posts: 39 Thanks: 0  Re: rings and fields Quote:
If a + bw = a' + b'w, with a, a', b, b', then w= (a'a)/(bb'), and this belongs to F ==> it HAS to be that b = b', and then a = a'. Regards Tonio  

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