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

(Bow)

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- Mar 11th 2010, 11:28 AMMathseisenstein 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

(Bow) - Mar 11th 2010, 02:14 PMTinyboss
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.

- Mar 12th 2010, 12:35 PM1234567