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Topic: Multiplication and addition of ideals
Replies: 7   Last Post: Feb 26, 2009 10:30 AM

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Posts: 1,133
Registered: 12/6/04
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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