Abstract:Let k be any algebraically closed field, and denote by k (( t )) the field of formal power series in one indeterminate t over k . Let so that K is the field of Puiseux expansions with coefficients in ...Let k be any algebraically closed field, and denote by k (( t )) the field of formal power series in one indeterminate t over k . Let so that K is the field of Puiseux expansions with coefficients in k (each element of K is a formal power series in t l/r for some positive integer r ). It is well-known that K is algebraically closed if and only if k is of characteristic zero [1, p. 61]. For examples relating to ramified extensions of fields with valuation [9, §6] it is useful to have a field analogous to K which is algebraically closed when k has non-zero characteristic p . In this paper, I prove that the set L of all formal power series of the form Σ a i t ei (where ( e i ) is well-ordered, e i = m i | np rt , n ∈ Ζ, m i ∈ Ζ, a i ∈ k , r i ∈ Ν) forms an algebraically closed field.Read More