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 April 3rd, 2010, 08:23 PM #1 Senior Member   Joined: Nov 2009 Posts: 129 Thanks: 0 ring compute the product in the given ring. (-3,5)(2,-4) in Z_4 x Z_11 least common multiple is lcm(-3,5)=-15 and lsm(2,-4)=-4. how do i find -15 in Z_4? and -4 in Z_11 if these was the right value.
 April 3rd, 2010, 09:13 PM #2 Senior Member   Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3 Re: ring Aren't products in the ring defined componentwise? I.e. (a,b)(c,d) = (ac,bd) How does lcm come into play?
 April 4th, 2010, 02:27 AM #3 Senior Member   Joined: Nov 2009 Posts: 129 Thanks: 0 Re: ring (-3,5)(2,-4)= (-6,-20) = lcm (-6,-20)= -60? What make me confuse is the negative sign. Do we treat it the same as if it was positive?
 April 4th, 2010, 05:09 PM #4 Senior Member   Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3 Re: ring I'm still not sure what lcm has to do with it-- you just take the product componentwise, and reduce... so (-6,-20). We need to reduce -6 (mod 4), and -20 (mod 11). 11|-22, and -20 = -22+2, so -20 = 2 (mod 11) Likewise -6=-8+2, and 4|-8, so -6=2(mod 4), so our answer is (2,2). Does that make sense?
 April 4th, 2010, 11:17 PM #5 Senior Member   Joined: Nov 2009 Posts: 129 Thanks: 0 Re: ring yes thanks so much.

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