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Multiplication and addition of ideals
Posted:
Feb 6, 2009 11:35 AM
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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 tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however 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
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