My Math Forum rings and fields

 Abstract Algebra Abstract Algebra Math Forum

 November 27th, 2007, 12:46 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, 02:49 AM   #2
Member

Joined: Dec 2006

Posts: 39
Thanks: 0

Re: rings and fields

Quote:
 Originally Posted by just17b 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.
*****************************************

If a + bw = a' + b'w, with a, a', b, b', then w= (a'-a)/(b-b'), and this belongs to F ==> it HAS to be that b = b', and then a = a'.

Regards
Tonio

 Tags fields, rings

« Rings | ring »

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post math interest22 Abstract Algebra 5 February 5th, 2014 06:30 AM alejandrofigueroa Abstract Algebra 1 November 17th, 2013 05:26 PM question Abstract Algebra 2 March 16th, 2012 08:17 PM emilie111 Abstract Algebra 1 March 6th, 2009 10:00 PM bjh5138 Abstract Algebra 0 December 4th, 2007 03:22 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top