tinynerdi

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.

cknapp

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

How does lcm come into play?

tinynerdi

(-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?

cknapp

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?

tinynerdi

yes thanks so much.