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Valuation Bases for Extensions of Valued Vector Spaces

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06_Valuation_bases_for_extensions_1996.pdf
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1996

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Forum Mathematicum. 1996, 8, pp. 723-735. Available under: doi: 10.1515/form.1996.8.723

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Let (V,v) be any valued vector space, and (V0,v) a subspace. Then (V,v) admits a valuation basis over (V0,v) if and only if it admits a nice composition series over (V0,v). We show that this is always the case if v(V\V0) is reversely well ordered. If v(V0) is reversely well ordered, we show that V0 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.

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510 Mathematik

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ISO 690KUHLMANN, Salma, 1996. Valuation Bases for Extensions of Valued Vector Spaces. In: Forum Mathematicum. 1996, 8, pp. 723-735. Available under: doi: 10.1515/form.1996.8.723
BibTex
@article{Kuhlmann1996Valua-595,
  year={1996},
  doi={10.1515/form.1996.8.723},
  title={Valuation Bases for Extensions of Valued Vector Spaces},
  volume={8},
  journal={Forum Mathematicum},
  pages={723--735},
  author={Kuhlmann, Salma}
}
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