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ringcompute 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. |

Re: ringAren't products in the ring defined componentwise? I.e. (a,b)(c,d) = (ac,bd) How does lcm come into play? |

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? |

Re: ringI'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? |

Re: ringyes thanks so much. |

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