We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
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.
