Need some help...

Let the ring of gaussian integers.

1)Show that

( means the ideal generated by )

2)Prove that the ideal on the right is prime.

Thank you folks!

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- Jan 15th 2009, 08:02 AMIntiRings and Ideals
Need some help...

Let the ring of gaussian integers.

1)Show that

( means the ideal generated by )

2)Prove that the ideal on the right is prime.

Thank you folks! - Jan 15th 2009, 04:42 PMNonCommAlg
- Jan 16th 2009, 04:35 AMInti
thereīs one thing thatīs not clear to me:

Iīve just proved that , which means that is isomorphic to , which is a field.

That allows me to say that the ideal is prime?

As far as Iīm concerned, the quotient of a ring by a prime ideal is a domain.

Iīm kind of confused with that...

But the help was very helpful (Nod)

And I have one more question: is the product of two ideals the set of all the products of the elements of each ideal??

Thanks! - Jan 16th 2009, 04:55 PMNonCommAlg
that means the ideal is maximal and we know that every maximal ideal is prime.

Quote:

And I have one more question: is the product of two ideals the set of all the products of the elements of each ideal??

for all