On the completion of real valued ternary fields (Q1840590)

The paper considers ternary fields endowed with a uniform valuation in the sense of \textit{F. Kalhoff} [Geom. Dedicata 28, 337-348 (1988; Zbl 0665.51001)]. In addition, it is assumed that the value loop is a subgroup of the multiplicative group of positive reals. The ternary operation extends uniquely to the complete hull of the underlying metric space, turning the latter into a ternary field with a uniform valuation. The author then shows the following. Any real-valued ternary field \((N,v,\Gamma_0)\) has a maximal dense extension, which is complete and unique up to isometric \(N\)-isomorphism. Therefore, any discretely valued ternary field \((N,v,Z_{-\infty})\) has a maximal immediate extension, which is spherically complete and unique up to isometric \(N\)-isomorphism.