In a valued fields book on page $82$ there is a question: "show that every non-trivial valuation of $\mathbb R$ has divisible value group and algebraically closed residue class field." How do I approach this problem? Thanks.
2026-03-28 10:28:05.1774693685
Non-trivial valuation of $\mathbb R$
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I think Theorem 3.2.11 of the book Valued Fields by Antonio J. Engler and Alexander Prestel, Springer, 2005, can be helpful.