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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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.
Originally Posted by Maths 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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