What does it mean: the product of two ideals I

Tiffany Russell

Tiffany Russell

Answered question

2021-12-10

What does it mean: the product of two ideals I and J is the set of all finite sums of elements of the form ab with aI and bJ?

Answer & Explanation

Terry Ray

Terry Ray

Beginner2021-12-11Added 50 answers

One would like the product ideal to be:
IJ={ijiI,jJ}
However, we can easily see that there is a problem. It must be closed under addition, so ij+i′j′ must be in IJ. Can you find iI, jJ such that ij+i′j′=i′′j′′ so that its
Mollie Nash

Mollie Nash

Beginner2021-12-12Added 33 answers

For example:
I=(2,X) and J=(3,X) in Z[X]. Then IJ=(6,X). Thus XIJ and X can't be written as ij with iI,jJ. (Note that if one of the ideals is principal one can't get such an example.)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?