![]() |
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.
|
![]() |
![]() |
|
Tags |
ring |
Thread Tools | |
Display Modes | |
|
![]() | ||||
Thread | Thread Starter | Forum | Replies | Last Post |
Ring | sebaflores | Abstract Algebra | 1 | October 27th, 2013 05:29 PM |
Ring | Mathew | Abstract Algebra | 5 | August 29th, 2010 09:53 PM |
Ring and pseudo-ring | cgouttebroze | Abstract Algebra | 5 | August 14th, 2008 01:04 PM |
ring | stf123 | Abstract Algebra | 3 | December 7th, 2007 08:47 AM |
ring | Frazier001 | Abstract Algebra | 1 | December 6th, 2007 02:21 PM |