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Minkowski's Lemma


Let R be a number ring of degree n with 2s imaginary embeddings. Then every ideal class of R contains an ideal J such that

 ||J||<=(n!)/(n^n)(4/pi)^ssqrt(|disc(R)|),

where ||J|| denotes the norm of J.


This entry contributed by David Terr

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References

Marcus, D. A. Number Fields, 3rd ed. New York: Springer-Verlag, p. 137, 1996.

Referenced on Wolfram|Alpha

Minkowski's Lemma

Cite this as:

Terr, David. "Minkowski's Lemma." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/MinkowskisLemma.html

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