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Math Help - eisenstein integers

  1. #1
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    eisenstein integers

    could someone kindly show me how Eisenstein integers are
    Euclidean domain.

    I know that Eisenstein integers forms a Euclidean domain whose norm N is given by

    Z[ω] = ring of Eisenstein integers
    f(a + bω) = a^2 - ab + b^2

    Thanks

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  2. #2
    Senior Member Tinyboss's Avatar
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    Show that it's an integral domain and that for any a and b, b nonzero, you can find q and r such that a=qb+r with r=0 or N(r)<N(b). Essentially, show that the Euclidean Algorithm works there.
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  3. #3
    Junior Member
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    Quote Originally Posted by Maths View Post
    could someone kindly show me how Eisenstein integers are
    Euclidean domain.

    I know that Eisenstein integers forms a Euclidean domain whose norm N is given by

    Z[ω] = ring of Eisenstein integers
    f(a + bω) = a^2 - ab + b^2

    Thanks

    Similar to gaussien integers
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