2 rings with a special property

From: Bessel (crypto_170_at_hotmail.com)
Date: 06/30/04 

Date: 29 Jun 2004 18:54:18 -0700

Hi,

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.

Any suggestions of where to start?

Thanks for advice.

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