Talk:Fractional ideal

Suggestions

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

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)[reply]

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)[reply]

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)[reply]

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{aligned}(2\zeta _{3}+1)^{2}&=4\zeta _{3}^{2}+4\zeta _{3}+1\\&=4(\zeta _{3}^{2}+\zeta _{3})+1\end{aligned}}

Since $\zeta _{3}$ satisfies $\zeta _{3}^{2}+\zeta _{3}=-1$ , our factorization makes sense.

Note that this factorization can be generalized by taking

{\begin{aligned}(n\zeta _{3}+1)^{2}&=2n\zeta _{3}^{2}+2n\zeta _{3}+1\\&=2n(\zeta _{3}^{2}+\zeta _{3})+1\\&=1-2n\end{aligned}}

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)[reply]

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)[reply]