On the Exponential and Logarithmic Functions in O-algebras
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.
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