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April 3rd, 2010, 08:23 PM   #1
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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.
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April 3rd, 2010, 09:13 PM   #2
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Re: ring

Aren't products in the ring defined componentwise? I.e. (a,b)(c,d) = (ac,bd)

How does lcm come into play?
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April 4th, 2010, 02:27 AM   #3
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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?
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April 4th, 2010, 05:09 PM   #4
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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?
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April 4th, 2010, 11:17 PM   #5
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Re: ring

yes thanks so much.
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