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Vector spaces with valuations. (English) Zbl 0318.15002


MSC:

15A03 Vector spaces, linear dependence, rank, lineability
20K40 Homological and categorical methods for abelian groups
46A40 Ordered topological linear spaces, vector lattices
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References:

[1] Bourbaki, N., Algèbre Commutative, (Graduations, filtrations et topologies (1961), Hermann: Hermann Paris), Chap. 3 · Zbl 0141.03501
[2] Brown, R., Valued vector spaces of countable dimension, Publ. Math. Debrecen, 18, 149-151 (1971) · Zbl 0254.15001
[3] Conrad, P. F., Embedding theorems for abelian groups with valuations, Amer. J. Math., 75, 1-29 (1953) · Zbl 0050.02303
[4] Fleischer, I., Maximality and ultracompleteness in normed modules, (Proc. Amer. Math. Soc., 9 (1958)), 151-158 · Zbl 0085.02501
[5] Fuchs, L., (Infinite Abelian Groups, vol. 1-2 (1970), Academic Press: Academic Press New York) · Zbl 0213.03501
[6] Gruson, L., Catégories d’espaces de Banach ultramétriques, Bull. Soc. Math. France, 94, 287-299 (1966) · Zbl 0149.34801
[7] Ingleton, A. W., The Hahn-Banach theorem for non-archimedean valued fields, (Proc. Camb. Phil. Soc., 48 (1972)), 41-45 · Zbl 0046.12001
[8] Monna, A. F., Analyse non-Archimédienne (1970), Springer: Springer Berlin · Zbl 0203.11501
[9] Ostrowski, A., Untersuchungen zur arithmetischen Theorie der Körper, Math. Z., 39, 269-404 (1935) · Zbl 0010.15001
[10] van der Put, M., Espaces de Banach non-archimédiens, Bull. Soc. Math. France, 97, 309-320 (1969) · Zbl 0193.40901
[11] Robert, P., On some non-archimedean normed linear spaces, Compositio Math., 19, 1-77 (1968) · Zbl 0153.44101
[12] D. E. Thomas; D. E. Thomas
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