Let $(K,varphi)$ be a perfect valued field of rank 1, let $overline{varphi}$ be an extension of the absolute (multiplicative) value $varphi$ to a fixed algebraic closure $overline{K}$ and let $| .|_{varphi}$ be the corresponding spectral norm on $K$. Let $(widetilde{overline{K}},| .|_{varphi}^{, ilde{}})$ be a fixed completion of $(overline{K},| .|_{varphi})$. In this paper we generalize a result of A. Ostrowski~[8] relative to the absorbent property of a subfield, from the case of a complete non-Archimedian valued field of characteristic 0 to our ring $(widetilde{overline{K}},| .|_{varphi}^{, ilde{}})$ (see Theorem 1, Theorem 4). We also apply these results to discuss in a more general context the following conjecture due to A. Zaharescu (2009): $langle$For any $x,yinmathbf{C}_{p}$-the complex $p$-adic field, there exists $tinmathbf{Q}_{p}$-the $p$-adic number field, such that $widetilde{mathbf{Q}_{p}(x,y)}=widetilde{mathbf{Q}_{p}(x+ty)}$, where $widetilde{L}$ means the $p$-adic topological closure of a subfield $L$ of $mathbf{C}_{p}$ in $mathbf{C}_{p} angle$.
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