FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups 
 ProfileProfile   PreferencesPreferences   Log in to check your private messagesLog in to check your private messages   Log inLog in 
Forum index » Science and Technology » Math » Undergraduate
Nature of a certian Ideal
Post new topic   Reply to topic Page 1 of 1 [4 Posts] View previous topic :: View next topic
Author Message
David C. Ullrich
science forum Guru


Joined: 28 Apr 2005
Posts: 2250

PostPosted: Mon Jul 03, 2006 8:24 am    Post subject: Re: Nature of a certian Ideal Reply with quote

On Sun, 02 Jul 2006 10:25:11 EDT, koltesagar <sagar.kolte@gmail.com>
wrote:

Quote:
consider the Ideal

I={set of all continous functions form R to R vanishing at 'a' , a fixed point }


in the ring of continous functions form R to R. with addition and multiplication being point wise.

R= set of real numbers

Is I principal?

No. If g is in I (and g is non-zero except at a) then there exists
f in I such that f/g -> infinity at a, hence f is not in the ideal
generated by g.

Quote:
Thank You.


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

David C. Ullrich
Back to top
Virgil
science forum Guru


Joined: 24 Mar 2005
Posts: 5536

PostPosted: Sun Jul 02, 2006 8:05 pm    Post subject: Re: Nature of a certian Ideal Reply with quote

In article
<8974198.1151853700195.JavaMail.jakarta@nitrogen.mathforum.org>,
koltesagar <sagar.kolte@gmail.com> wrote:

Quote:
consider the Ideal

I={set of all continous functions form R to R vanishing at 'a' , a fixed
point }


in the ring of continous functions form R to R. with addition and
multiplication being point wise.

R= set of real numbers

Is I principal?

Thank You.

One would have to have some fixed function f:R --> R with f in I so that
for every g in I, g = h*f for some h in the ring.

But for every such g, one would have to have that g/f must have a finite
limit as x --> a.

Consider g = real cube root of f,so g will be in I whenever f is in I.

What is lim_{x --> a} g(x)/f(x) like?
Back to top
William Elliot
science forum Guru


Joined: 24 Mar 2005
Posts: 1906

PostPosted: Sun Jul 02, 2006 4:03 pm    Post subject: Re: Nature of a certian Ideal Reply with quote

On Sun, 2 Jul 2006, koltesagar wrote:

Quote:
consider the Ideal

I={set of all continous functions form R to R vanishing at 'a' , a fixed
point }

I = { f in C(R,R) | f(a) = 0 }

Quote:
in the ring of continous functions form R to R. with addition and
multiplication being point wise.

R= set of real numbers
Is I principal?

Some g with for all f,

f(a) = 0 iff some h in C(R,R) with f = g*h ?

No. Notice g(a) = 0, sqr g in I.
some h with sqr g = g * h
h = (sqr g)/g is not continuous.
Back to top
Sagar Kolte
science forum beginner


Joined: 14 Apr 2005
Posts: 31

PostPosted: Sun Jul 02, 2006 2:25 pm    Post subject: Nature of a certian Ideal Reply with quote

consider the Ideal

I={set of all continous functions form R to R vanishing at 'a' , a fixed point }


in the ring of continous functions form R to R. with addition and multiplication being point wise.

R= set of real numbers

Is I principal?

Thank You.
Back to top
Google

Back to top
Display posts from previous:   
Post new topic   Reply to topic Page 1 of 1 [4 Posts] View previous topic :: View next topic
The time now is Sun Mar 02, 2014 3:18 pm | All times are GMT
Forum index » Science and Technology » Math » Undergraduate
Jump to:  

Similar Topics
Topic Author Forum Replies Last Post
No new posts JSH: Truth is the highest ideal jstevh@msn.com Math 9 Thu Jul 20, 2006 5:18 am
No new posts On the Structure of Particles and the Nature of Nuclear F... zhouyb_8@163.com Strings 0 Sat Jul 15, 2006 10:55 am
No new posts Nature of proofs by induction un student Undergraduate 10 Sat Jul 01, 2006 7:59 am
No new posts On the Structure of Particles and the Nature of Nuclear F... zhouyb_8@163.com Relativity 0 Sun Jun 25, 2006 2:35 am
No new posts What is quantum mechanics trying to tell us about the nat... koantum Research 0 Thu Jun 08, 2006 8:07 am

Copyright © 2004-2005 DeniX Solutions SRL
Other DeniX Solutions sites: Electronics forum |  Medicine forum |  Unix/Linux blog |  Unix/Linux documentation |  Unix/Linux forums  |  send newsletters
 


Powered by phpBB © 2001, 2005 phpBB Group
[ Time: 0.0988s ][ Queries: 20 (0.0669s) ][ GZIP on - Debug on ]