Let $(V,v)$ be any valued vector space, and $(V_0,v)$ a subspace. Then $(V,v)$ admits a valuation basis over $(V_0,v)$ if and only if it admits a nice composition series over $(V_0,v)$. We show that this is always the case if $v(V\setminus V_0)$ is reversely well ordered. If $v(V_0)$ is reversely well ordered, we show that $V_0$ is nice in any extension, and that it admits a valuation basis over every subspace. Finally, we show that the property of admitting a valuation basis is preserved under countable dimensional extensions.

Last update: February 4, 1999