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Math Help - integer?

  1. #1
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    integer?

    what does it mean by integer/ m integer?

    im asked to find all the units of integer/ 12 integer and im not sure what does that mean.

    thanks
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    what does it mean by integer/ m integer?

    im asked to find all the units of integer/ 12 integer and im not sure what does that mean.

    thanks
    I'm not certain what you mean by "integer/12 integer" but I suspect you mean \mathbb{Z}_{12}, the "integers modulo 12". The "units of a ring" are those members of ring that have a multiplicative inverse. It should be easy to see that if a number has a common factor with 12, then some multiple of it will be a multiple of 12, so congruent to 0 modulo 12, so cannot have a multiplicative inverse.
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  3. #3
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    does it mean that for example in integer modulo 12, [2] will not have an inverse since gcd of 12 and 2 is not 1?
    so units of a ring are [5], [7],[11]?
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  4. #4
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    More to the point, [2] does not have an inverse (and so is not a unit) because [2][6]= [0]. Of course, that is a direct result of the fact that gcd(2, 12)= 2 not 1.

    [5], [7], and [11] are units but you are missing one obvious one. Remember that the set of all units of a ring form a group with multiplication.
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  5. #5
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    hmmm i dont get what does it mean by the set of all units of a ring form a group with multiplication. does it mean that [5],[7],[11] are cyclic groups that will generate interger 12?
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