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On the Exponential and Logarithmic Functions in O-algebras

  • Lluís Puig
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

Here, we assume that the quotient field K of O has characteristic zero. If O contains a primitive p-th root of unity ξ then, in suitable ideals of the commutative O-algebras, we can consider the so-called exponential function. As usual, this function is a homomorphism from the additive structure to the multiplicative one; in particular, the multiplication by n ∈ ℕ becomes the n-th power, and thus this function is helpful in proving the existence of the n-th root of some elements. In §14 and §15, we need this kind of results; in this section, we will prove them.

Keywords

Exponential Function Power Function Finite Group Characteristic Zero Logarithmic Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Lluís Puig
    • 1
  1. 1.Institut de Mathématiques de JussieuUniversité de Paris 7 — Denis DiderotParisFrance

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