Talk:Fractional ideal

Suggestions
An explicit example of a fractional ideal would be nice. (basically added) --Rschwieb 18:15, 4 July 2006 (UTC)


 * Yes, most definitely: Can someone who is knowledgeable about the subject please include several examples.50.205.142.50 (talk) 23:16, 24 May 2020 (UTC)

Also, some sources: Mline's notes from his web page are pretty useful and informative. Then there's Neukirch's book "Algebraic Number Theory"

Someone wrote a section in TeX, not realizing that TeX doesn't quite work like that, here. John Baez (talk) 19:23, 17 July 2009 (UTC)

Mangled sentence
The second sentence in the section Number fields is as follows:

"We call a fractional ideal which is a subset of $$\mathcal{O}_K$$ integral."

I hope someone knowledgeable about fractional ideals can rewrite that sentence in English.50.205.142.50 (talk) 23:14, 24 May 2020 (UTC)

Third example
The article currently reads (following an edit by Kaptain-k-theory):

"In $$\mathbb{Q}_{\zeta_3}$$ we have the factorization $$(3) = (2\zeta_3 + 1)^2$$. This is because if we multiply it out, we get
 * $$\begin{align}

(2\zeta_3 + 1)^2 &= 4\zeta_3^2 + 4\zeta_3 + 1 \\ &= 4(\zeta_3^2 + \zeta_3) + 1 \end{align}$$ Since $$\zeta_3$$ satisfies $$\zeta_3^2 + \zeta_3 =-1$$, our factorization makes sense.

Note that this factorization can be generalized by taking
 * $$\begin{align}

(n\zeta_3 + 1)^2 &= 2n\zeta_3^2 + 2n\zeta_3 + 1 \\ &= 2n(\zeta_3^2 + \zeta_3) + 1 \\ &= 1 - 2n \end{align}$$ giving a factorization of all ideal generated by an odd number $$1+2k$$ (with $$k = -n$$)."

Surely the last part of this is complete nonsense – it should be $$(n\zeta_3 + 1)^2 = n^2\zeta_3^2 + 2n\zeta_3 + 1 = n(n\zeta_3^2 + 2\zeta_3) + 1$$. I have therefore removed this part from the article. Joel Brennan (talk) 18:54, 28 March 2022 (UTC)

Bare URL
I corrected the bare URL by replacing the bare URL with a reference to a textbook, Barucci, Valentina (2000). Also, the link provided by the bare URL was non-functioning. For more information see WP:BAREURLS. TMM53 (talk) 23:05, 15 March 2023 (UTC)