Hello, Im trying to prove that the product of two non principal ideals is a principal ideal.
I consider the non principals ideals
The book saids the result is (3). But I don`t know how to do the product.
Regards...
the elements of IJ are sums of the form Σij, where i is in I, and j is in J. what are the possible products ij?
(3)(3) = 9
(3)(1 + √(-5))
(1 - √(-5))(3)
(1 - √(-5)(1 + √(-5)) = 1 - (-5) = 6.
3 divides all of these products, so certainly IJ is contained in (3).
on the other hand 3 = 9 - 6 which is an element of IJ, so (3) is contained in IJ.