Valuation bases for generalized algebraic series fields

a r t i c l e i n f o a b s t r a c t Keywords: Valuation independence Generalized series fields Fields of Puiseux series Restricted exponential function We investigate valued fields which admit a valuation basis. Given a countable ordered abelian group G and a real closed or algebraically closed field F with subfield K , we give a sufficient condition for a valued subfield of the field of generalized power series F ((G)) to admit a K-valuation basis. We show that the field of rational functions F (G) and the field F (G) ∼ of power series in F ((G)) algebraic over F (G) satisfy this condition. It follows that for archimedean F and divisible G the real closed field F (G) ∼ admits a restricted exponential function.