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arXiv · 1302.1381

Tensor products of valued fields

Itaï Ben Yaacov
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Abstract

We give a short argument why the tensor product valuation on $K \otimes_k L$ is multiplicative when $k$ is an algebraically closed valued field and $K$ and $L$ are valued extensions (all valuations being in $\bR$). When the valuation on $k$ is non trivial we use the fact that $ACVF$, the theory of algebraically closed (non trivially) valued fields, has quantifier elimination.

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Itaï Ben Yaacov. 2014-10-12. Tensor products of valued fields. https://doi.org/10.1112/blms%2Fbdu092

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