Contents
Research Article
Manifold-Valued Holomorphic Approximation
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- Published online by Cambridge University Press:
- 20 November 2018, pp. 370-380
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A Short Note on the Higher Level Version of the Krull–Baer Theorem
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- Published online by Cambridge University Press:
- 20 November 2018, pp. 381-384
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Klep and Velušček generalized the Krull–Baer theorem for higher level preorderings to the non-commutative setting. A
$n$-real valuation 
$v$ on a skew field 
$D$ induces a group homomorphism 
$\overline{v}$. A section of $\overline{v}$ is a crucial ingredient of the construction of a complete preordering on the base field $D$ such that its projection on the residue skew field 
${{k}_{v}}$ equals the given level 1 ordering on ${{k}_{v}}$. In the article we give a proof of the existence of the section of $\overline{v}$, which was left as an open problem by Klep and Velušček, and thus complete the generalization of the Krull–Baer theorem for preorderings.
