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...

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- June 10th 2011, 09:31 PMorbitProduct of non principal ideals is principal.
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... - June 11th 2011, 03:33 AMtonio
- June 11th 2011, 07:43 AMorbit
- June 11th 2011, 08:38 PMtonio
- June 11th 2011, 08:51 PMDeveno
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. - June 12th 2011, 02:17 PMorbitThanks