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Multiplication and addition of ideals
Posted:
Feb 6, 2009 11:35 AM


Here's an idle thought I had many years ago but never bothered to follow up on. Ideals in a ring R can be multiplied. They can also be added; I + J is the ideal generated by I and J. Multiplication of ideals distributes over addition. However, we don't have additive inverses. So it seems that the ideals of R form a semiring. Does studying the structure of this semiring tell us anything useful about the structure of R?
A casual search hasn't turned up the answer to my question, but maybe I'm not looking in the right places. Or maybe it's just not a useful idea.  Tim Chow tchowatalumdotmitdotedu The range of our projectileseven ... the artilleryhowever great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. Galileo, Dialogues Concerning Two New Sciences



