Re: 2 rings with a special property
From: William Elliot (marsh_at_privacy.net)
Date: 06/30/04
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Date: Wed, 30 Jun 2004 01:09:51 -0700
On Tue, 29 Jun 2004, Bessel wrote:
>
> I want to find two rings R1, R2 and a homomorphism f: R1-->R2 between
> the two rings. I need some special properties:
>
> 1. R1 should have many ideals
> 2. Kernel of f should not look too "special" in any way.
> I.e. for example if we are dealing with matrices and the kernel of
> homomorphism is such that last column or last row is all zeroes, then
> it's not quite satisfactory because then it looks "special" as opposed
> to other regular elements which don't have this 0s property.
> 3. I also would like |ker f|/|R1| to be fairly small.
>
identity:Z -> Z.
Z has infintely many ideals, kernel = {0}, |ker|/|Z| = 0
otherwise if division by |R1| is clue R1 is finite
identity:Z_n -> Z_n
Z_n has lots of ideals when n has lots of factors. Again
kernel = {0} is most simple and |ker|/|Z_n| -> 0 as n -> oo
> Any suggestions of where to start?
>
Plug the leaks in the problem statement?
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