Thread: 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

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