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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
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807:{\displaystyle {\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}}}
130:
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Also, some sources: Mline's notes from his web page are pretty useful and informative. Then there's
Neukirch's book "Algebraic Number Theory"
527:{\displaystyle {\begin{aligned}(2\zeta _{3}+1)^{2}&=4\zeta _{3}^{2}+4\zeta _{3}+1\\&=4(\zeta _{3}^{2}+\zeta _{3})+1\end{aligned}}}
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Yes, most definitely: Can someone who is knowledgeable about the subject please include several examples.
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1025:{\displaystyle (n\zeta _{3}+1)^{2}=n^{2}\zeta _{3}^{2}+2n\zeta _{3}+1=n(n\zeta _{3}^{2}+2\zeta _{3})+1}
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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Someone wrote a section in TeX, not realizing that TeX doesn't quite work like that, here.
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I hope someone knowledgeable about fractional ideals can rewrite that sentence in
English.
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An explicit example of a fractional ideal would be nice. (basically added) --
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The article currently reads (following an edit by
Kaptain-k-theory):
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Surely the last part of this is complete nonsense – it should be
817:
giving a factorization of all ideal generated by an odd number
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Note that this factorization can be generalized by taking
1032:. I have therefore removed this part from the article.
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373:. This is because if we multiply it out, we get
218:We call a fractional ideal which is a subset of
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611:{\displaystyle \zeta _{3}^{2}+\zeta _{3}=-1}
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305:{\displaystyle \mathbb {Q} _{\zeta _{3}}}
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366:{\displaystyle (3)=(2\zeta _{3}+1)^{2}}
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95:This article is within the scope of
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38:It is of interest to the following
242:{\displaystyle {\mathcal {O}}_{K}}
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1084:Mid-priority mathematics articles
618:, our factorization makes sense.
115:Knowledge:WikiProject Mathematics
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109:and see a list of open tasks.
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557:{\displaystyle \zeta _{3}}
312:we have the factorization
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868:{\displaystyle k=-n}
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839:{\displaystyle 1+2k}
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59:Mathematics
30:Start-class
1073:Categories
564:satisfies
249:integral.
192:John Baez
1047:Bare URL
164:Rschwieb
139:on the
846:(with
537:Since
36:scale.
1057:TMM53
1061:talk
1038:talk
875:)."
276:"In
260:talk
196:talk
178:talk
1055:.
131:Mid
1075::
1063:)
1040:)
1005:ζ
984:ζ
956:ζ
932:ζ
893:ζ
860:−
792:−
760:ζ
742:ζ
706:ζ
682:ζ
643:ζ
603:−
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251:"
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1059:(
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918:=
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886:(
863:n
857:=
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834:k
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786:=
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738:(
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729:=
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329:=
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258:(
235:K
229:O
216:"
194:(
176:(
143:.
42::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
