Dummit and Foote (D&F), Ch15, Section 15.1, Exercise 15 reads as follows:

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If and ,

show that is the product ideal

where and .

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I am having trouble getting started on this problem.

One issue/problem I have is - what is the exact nature of and . What (explicitly) are the nature of the elements of these ideals.

I would appreciate some help and guidance.

Peter

Note: D&F define as follows:

for all