Re: Prime ideal in Z[sqrt{-5}]
- From: Timothy Murphy <tim@xxxxxxxxxxxxxxxxxxxxxx>
- Date: Mon, 09 Oct 2006 01:58:15 +0100
James wrote:
I'm having trouble showing something very basic : Why is the ideal (2, 1 +
sqrt{-5}) a prime ideal in Z[sqrt{-5}]?
It's probably easiest to show that it is maximal (and so prime).
Take any element x = a + b sqrt(-5).
Show that you can add multiples of 2 and 1 + sqrt{-5}
to get either 0 (in which case x is in the ideal) or else 1.
--
Timothy Murphy
e-mail (<80k only): tim /at/ birdsnest.maths.tcd.ie
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland
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