- #1
fischer
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I want to answer this question:
Find all the ideals of the direct product of rings R \times S.
(I think this means show that the ideals are I \times J where I, J are ideals of R, S, respectively.)
I think the problem is that I don't know how to show that any ideal of R \times S is of the form A \times B, where A \subset R, B \subset S. Showing that each are ideals should follow easily enough.
So I made attemps to prove that (a, m), (b, n) \in K iff (a, n), (b, m) \in K (where K is an ideal of R \times S), without success...
can someone help me out?
thanks in advance.
Find all the ideals of the direct product of rings R \times S.
(I think this means show that the ideals are I \times J where I, J are ideals of R, S, respectively.)
I think the problem is that I don't know how to show that any ideal of R \times S is of the form A \times B, where A \subset R, B \subset S. Showing that each are ideals should follow easily enough.
So I made attemps to prove that (a, m), (b, n) \in K iff (a, n), (b, m) \in K (where K is an ideal of R \times S), without success...
can someone help me out?
thanks in advance.
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