Re: Question on integral extensions,,

In article <di6058$bmfk$1@xxxxxxxxxxxxxxxxx>, James <James545@xxxxxxxxx> wrote:
>It is true that if S is a finitely generated R-module, then S is an integral
>extension of R. But it was claimed in my class today that the other
>direction is true as well.
>
>But isn't Q-bar integral over Q,

Yes.

>but Q-bar is an infinite dimensional vector
>space over Q, so it is not finitely generated as a Q-module?

What was the exact statement made? Surely not that "If S is an
integral extension of R, then S is a finitely generated R-module".

What is true is the following:

"If S is an integral extension of R, then for every s in S, R[s] is a
finitely generated R-module."



--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================

Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx

.

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