Re: 2 rings with a special property

From: Michael Amling (nospam_at_nospam.com)
Date: 06/30/04 

Date: Wed, 30 Jun 2004 14:35:33 GMT

William Elliot wrote:
> 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

   That kernel looks "special" to me. Dr. Israel's suggestion looks much
better (and I'm not just saying that because he's a U of C alum).

>
> 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?

--Mike Amling

Relevant Pages

  • Re: About characters on H^{oo}
    ... unit disk with the natural product, ... a homomorphicm of H^into C, i.e. character. ... maximal ideals ... from A onto A/I is actually a complex homomorphism ...
    (sci.math)
  • Re: F-algebra homomorphism
    ... homomorphism, it must be a function equal to its own square. ...   If A is an element of U and B is a subset of X ... is an evaluation map exactly when U is a principal ... the ideals must be maximal. ...
    (sci.math)
  • Re: Adultery and Sin
    ... Theory can be cold and impersonal and deal with ideals. ... In practice you ... are dealing with people - messy, complicated, human. ...
    (uk.religion.christian)
  • 2 rings with a special property
    ... the two rings. ... I need some special properties: ... R1 should have many ideals ... Kernel of f should not look too "special" in any way. ...
    (sci.crypt)
  • 2 rings with a special property
    ... the two rings. ... I need some special properties: ... R1 should have many ideals ... Kernel of f should not look too "special" in any way. ...
    (sci.math)