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finitely generated modules vs.finitely generated algebras
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michael friedman  
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  More options Jul 4, 7:29 am
Newsgroups: sci.math
From: michael friedman <ois3...@hotmail.com>
Date: Fri, 04 Jul 2008 07:29:46 EDT
Local: Fri, Jul 4 2008 7:29 am
Subject: finitely generated modules vs.finitely generated algebras
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hello everyone!

suppose A is a ring. I'm trying to understand the difference between a finitely
generated A-module and a finitely generated  A-algebra. what is the general
form of each? can you give an example of a
finitely generated  A-algebra which is not a finitely generated A-module ?

thanks
michael


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Jannick Asmus  
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  More options Jul 4, 7:53 am
Newsgroups: sci.math
From: Jannick Asmus <jannick.n...@web.de>
Date: Fri, 04 Jul 2008 13:53:42 +0200
Local: Fri, Jul 4 2008 7:53 am
Subject: Re: finitely generated modules vs.finitely generated algebras
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On 04.07.2008 13:29, michael friedman wrote:

> hello everyone!

> suppose A is a ring. I'm trying to understand the difference between a finitely
> generated A-module and a finitely generated  A-algebra. what is the general
> form of each? can you give an example of a
> finitely generated  A-algebra which is not a finitely generated A-module ?

A[X] - the polynomial ring in one indeterminate over A.

> thanks
> michael

--
Best wishes,
J.

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