Re: R[X,Y] polynomial ring
- From: magidin@xxxxxxxxxxxxxxxxx (Arturo Magidin)
- Date: Tue, 24 May 2005 18:32:33 +0000 (UTC)
In article <d6vrpm$j4s$1@xxxxxxxxxxxxxxxxxx>,
Mike <Mike_jones@xxxxxxxxx> wrote:
>> Mike <Mike_jones@xxxxxxxxx> wrote:
>>>ah i see, a quick query
>>>the ideal
>>>reals -R[X][1+X^2] what does this ideal look like?
>>
>> Huh?
>>
>> Do you mean, R[X](1+X^2)? I.e., all multiples of 1+X^2?
>>
>> It looks like all multiples of 1+X^2. They are exactly the polynomials
>> of R[X] which have the complex number i as a root.
>yeah sorry
>so does that mean it consists of
>{1+x^2, x+x^3, .......}
Again: please do not use lower and upper case interchangeably. Pick
one, and stick to it. Most mathematicians would consider "x" to be
something very different from "X".
It includes those, and many others. It also includes X^4-1 (which is
(1+X^2)(1-X^2)); it includes X^3 + X^2 + X + 1 (which is
(1+X^2)(1+X)), etc.
--
======================================================================
"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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