Valuation bases for extensions of valued vector spaces

Salma Kuhlmann
1996 Forum mathematicum  
Let (V v ) b e a n y v alued 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 s h o w that this is always the case if v(V nV 0 ) i s r e v ersely 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
more » ... eserved under countable dimensional extensions.
doi:10.1515/form.1996.8.723 fatcat:hjmhm7sp6beblm25mvx2skn5cm