Submission date: 6 February 2013.

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 R). 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.

Mathematics Subject Classification:

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Full text arXiv 1302.1381: pdf, ps.