In mathematics, a cyclotomic unit is a unit of an algebraic number field of the form (ζⁿ−1)/(ζ−1) for ζ a root of unity, or more generally a unit that can be written as a product of these and a root of unity. In Mathematics, a unit in a ( Unital) ring R is an invertible element of R, i In Mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) Field extension of the In Mathematics, the n th roots of unity, or de Moivre numbers are all the Complex numbers that yield 1 when raised to a given power

The cyclotomic units form a subgroup of finite index in the group of units of a cyclotomic field. In Algebraic number theory, Dirichlet 's unit theorem determines the rank of the Group of units in the ring O K In Number theory, a cyclotomic field is a Number field obtained by adjoining a complex Root of unity to Q, the field of Rational numbers In the case of prime power conductor this index is 1.

See also

• Elliptic unit

References

• Serge Lang Cyclotomic Fields I and II ISBN 0-387-96671-4 Springer Verlag Dec 1, 1989
• Lawrence C. In Mathematics, elliptic units are certain units of Abelian extensions of Imaginary quadratic fields constructed using singular values of Modular functions Serge Lang ( May 19, 1927 – September 12, 2005) was a French -born American Mathematician. Springer Science+Business Media or Springer (ˈʃpʁɪŋɐ is a worldwide Publishing company based in Germany, which publishes textbooks academic Washington Introduction to Cyclotomic Fields ISBN 0-387-94762-0 Springer Dec 1, 1996

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