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cliomseerg@kriocoucke.mai
science forum Guru Wannabe

Joined: 25 Oct 2005
Posts: 128

Posted: Fri Jul 21, 2006 10:08 am    Post subject: Sum of radical ideals

Dear NG,

Is there an integral domain by which the sum of two radical ideal is
not a radical ideal?

Sincerely,
Jose Capco
cliomseerg@kriocoucke.mai
science forum Guru Wannabe

Joined: 25 Oct 2005
Posts: 128

Posted: Fri Jul 21, 2006 10:18 am    Post subject: Re: Sum of radical ideals

Jose Capco wrote:
 Quote: Dear NG, Is there an integral domain by which the sum of two radical ideal is not a radical ideal? Sincerely, Jose Capco

Ok... I think I have the answer. Sorry, was a silly question..

Take the integral domain Z (the whole numbers) .. then 2Z is radical
and 2Z+2Z isnt.

Sincerely,
Jose Capco
David C. Ullrich
science forum Guru

Joined: 28 Apr 2005
Posts: 2250

Posted: Fri Jul 21, 2006 10:54 am    Post subject: Re: Sum of radical ideals

On 21 Jul 2006 03:18:25 -0700, "Jose Capco"
<cliomseerg@kriocoucke.mailexpire.com> wrote:

 Quote: Jose Capco wrote: Dear NG, Is there an integral domain by which the sum of two radical ideal is not a radical ideal? Sincerely, Jose Capco Ok... I think I have the answer. Sorry, was a silly question.. Take the integral domain Z (the whole numbers) .. then 2Z is radical and 2Z+2Z isnt.

??? Even though I have no idea what a radical ideal is it's
clear to me that this is false.

 Quote: Sincerely, Jose Capco

************************

David C. Ullrich
yuriart10
science forum beginner

Joined: 04 Nov 2010
Posts: 1
Location: USA

Posted: Fri Nov 05, 2010 1:49 am    Post subject: Re: Sum of radical ideals

Jose Capco wrote:
Jose Capco wrote:
 Quote: Dear NG, Is there an integral domain by which the sum of two radical ideal is not a radical ideal? Sincerely, Jose Capco

Ok... I think I have the answer. Sorry, was a silly question..

Take the integral domain Z (the whole numbers) .. then 2Z is radical
and 2Z+2Z isnt.

Sincerely,
Jose Capco

Thanks you for the post
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