Re: On the primeness of the union of a chain of prime ideals.
- From: Marc Olschok <sa796ol@xxxxxxxxxxxxxxxxxxxxxx>
- Date: 19 Oct 2005 11:45:01 -0400
freedom641@xxxxxxxxx <freedom641@xxxxxxxxx> wrote:
>
> Dear All,
>
> Clearly in commutative case, the union any chain of prime ideals is
> prime. Is it true in non-commutative case!?
Why not? The usual proof does not use commutativity.
If I and J are two ideals _not_ contained in the union,
then there are x in I, y in J and some prime ideal p in the chain,
such that x and y are not in p.
Marc
.
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