Explaining Why Z[-7] Is Not a Euchlidean Domain

[ElDavidas]

I know this is a physics forum but I've got a quick question about a Euchlidean domain:

Assuming that 1 - \sqrt {-7}and 2 are irreduclible, explain whyZ[-7] is not a euchlidean domain?

This is a pure maths question and I've asked questions about other pure maths courses and got decent answers.

Thanks

 

[Muzza]

There is no h in Euclidean.

If Z[-7] were Euclidean, then in particular all irreducible elements would be prime. This leads to a contradiction.

 

[matt grime]

Try multiplying 1-sqrt(-7) by its complex conjugate too.