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Sum of radical ideals
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cliomseerg@kriocoucke.mai
science forum Guru Wannabe


Joined: 25 Oct 2005
Posts: 128

PostPosted: Fri Jul 21, 2006 10:08 am    Post subject: Sum of radical ideals Reply with quote
Dear NG,

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

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


Joined: 25 Oct 2005
Posts: 128

PostPosted: Fri Jul 21, 2006 10:18 am    Post subject: Re: Sum of radical ideals Reply with quote
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
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David C. Ullrich
science forum Guru


Joined: 28 Apr 2005
Posts: 2250

PostPosted: Fri Jul 21, 2006 10:54 am    Post subject: Re: Sum of radical ideals Reply with quote
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
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yuriart10
science forum beginner


Joined: 04 Nov 2010
Posts: 1
Location: USA
PostPosted: Fri Nov 05, 2010 1:49 am    Post subject: Re: Sum of radical ideals Reply with quote
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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