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    So I was thinking. In the Rational field, are not all numbers units?

    Because every single number has an inverse. Then dos that not mean every single number are associates to each other?

    Thanks
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    (Original post by 2710)
    So I was thinking. In the Rational field, are not all numbers units?

    Because every single number has an inverse. Then dos that not mean every single number are associates to each other?

    Thanks
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    Ah ok. So every number excluding 0 are units? And are all associates of each other?
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    (Original post by 2710)
    So I was thinking. In the Rational field, are not all numbers units?

    Because every single number has an inverse. Then dos that not mean every single number are associates to each other?

    Thanks
    In any field, every non-zero element is a unit. This is part of the definition of a field.

    If R is more generally a division ring and r,s \in R are non-zero, then

    r = rs^{-1}s

    and clearly rs^{-1} is a unit.
 
 
 
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