On embeddability of uniformly valued ternary fields in Hahn ternary fields (Q1430542)

The author generalizes results of his previous paper [J. Geom. 71, No. 1--2, 162--181 (2001; Zbl 1011.51002)] about the embeddability of uniformly valued ternary fields \(N=(N,\nu,\Gamma_{0})\) into some Hahn ternary field of formal power series with coefficients in the residue ternary field and exponents in the value loop. He derives a necessary and sufficient condition for \(N\) to be embeddable and proves that if \(N\) is embeddable, then the following statements are equivalent: (i) the valuation \(\nu\) of \(N=(N,\nu,\Gamma_{0})\) is maximal, (ii) \(N=(N,d_\nu,\Gamma_{0})\) is completely spherical, and (iii) \(N=(N,\nu,\Gamma_{0})\) is isometrically isomorphic to some Hahn ternary field \((H,\nu_{H}, \Gamma_{0})\) on \(\Gamma\) over \(N_\nu\). Similar conditions are given for richer algebraic structures such as Cartesian groups, division algebras, skew fields, and fields.