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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

An isomorphism theorem for valuated vector spaces


Author: Paul Hill
Journal: Proc. Amer. Math. Soc. 88 (1983), 587-590
MSC: Primary 18B99; Secondary 18E05, 18G05, 20K99, 46N05
MathSciNet review: 702280
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Abstract: The following isomorphism theorem is proved for valuated vector spaces. Let $ N$ and $ N'$ be nice subspaces of free valuated vector spaces $ F$ and $ F'$, respectively. If $ N$ and $ N'$ have isomorphic basic subspaces and if the quotient spaces $ F/N$ and $ F'/N'$ are isomorphic, there exists an isomorphism from $ F$ onto $ F'$ that maps $ N$ onto $ N'$ and induces the given isomorphism on the quotient spaces. In particular, $ N$ and $ N'$ are isomorphic.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0702280-1
PII: S 0002-9939(1983)0702280-1
Keywords: Valuated vector space, basis, nice subspace of free space (NSF-space), isomorphism, uniqueness theorem
Article copyright: © Copyright 1983 American Mathematical Society