Re: Noetherian

In article <1146536420.493419.238940@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
trusiki@xxxxxxxxx wrote:

How do I show that the ring of continuous real valued functions on
[0,1] is not Noetherian?

The most direct way is to show that it contians an infinite descending
chain of ideals.

Can you show that for any finite but not empty subset of [0,1], the set
of continuous functions vanishing on that set is an ideal in your ring,
and the larger the subset, the smaller the ideal?
.

Relevant Pages

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