Let R and D be two division rings, then we know that in general every ideal of

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Let R and D be two division rings, then we know that in general every ideal of RxD has the form IxJ where I is an ideal of R and J an ideal of D.
How to show that every left or right-ideal of RxD is principle?
I know the only ideals of R and D are the trivials since they are division rings, but they may include left or right-ideals

Posted Date: Dec 03, 2021 12:02 AM

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Let R and D be two division rings, then we know that in general every ideal of

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Ideal Product redirects here For products named Ideal see Ideal disambiguation In ring theory a branch of abstract algebra an ideal of a ring is a special subset of its elements Ideals generalize cert... View the full answer

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