location:  Publications → journals → CMB
Abstract view

# A Short Note on the Higher Level Version of the Krull--Baer Theorem

Published:2010-08-19
Printed: Jun 2011
• Dejan Velušček,
University of Ljubljana, Faculty of Mathematics and Physics, Department of Mathematics, Ljubljana, Slovenia
 Format: HTML LaTeX MathJax PDF

## Abstract

Klep and Velu\v{s}\v{c}ek 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 Velu\v{s}\v{c}ek, and thus complete the generalization of the Krull--Baer theorem for preorderings.
 Keywords: orderings of higher level, division rings, valuations
 MSC Classifications: 14P99 - None of the above, but in this section 06Fxx - Ordered structures

 top of page | contact us | privacy | site map |