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

Published online by Cambridge University Press:  20 November 2018

Dejan Velušček*
Affiliation:
University of Ljubljana, Faculty of Mathematics and Physics, Department of Mathematics, Ljubljana, Sloveniae-mail: dejan.veluscek@fmf.uni-lj.si
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2011

References

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