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

Canadian mathematical bulletin

Dejan Velušček¹ 

[1] University of Ljubljana, Faculty of Mathematics and Physics, Department of Mathematics, Ljubljana, Slovenia

关键词: orderings of higher level;    division rings;    valuations;   

DOI  :  10.4153/CMB-2010-095-0

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Klep and Veluv{s}v{c}ek generalized the Krull--Baer theorem forhigher level preorderings to the non-commutative setting. A $n$-real valuation$v$ on a skew field $D$ induces a group homomorphism $overline{v}$. A sectionof $overline{v}$ is a crucial ingredient of the construction of a completepreordering on the base field $D$ such that its projection on the residue skewfield $k_v$ equals the given level $1$ ordering on $k_v$. In the article we givea proof of the existence of the section of $overline{v}$, which was left as anopen problem by Klep and Veluv{s}v{c}ek, and thuscomplete the generalization of the Krull--Baer theorem for preorderings.

【 授权许可】

Unknown