April 3rd, 2010, 07:23 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, 08:13 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, 01:27 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, 04:09 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). 1122, and 20 = 22+2, so 20 = 2 (mod 11) Likewise 6=8+2, and 48, so 6=2(mod 4), so our answer is (2,2). Does that make sense? 
April 4th, 2010, 10:17 PM  #5 
Senior Member Joined: Nov 2009 Posts: 129 Thanks: 0  Re: ring
yes thanks so much.


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