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

DOI:
https://doi.org/10.1090/S0002-9939-1983-0702280-1

MathSciNet review:
702280

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Abstract | References | Similar Articles | Additional Information

Abstract: The following isomorphism theorem is proved for valuated vector spaces. Let and be nice subspaces of free valuated vector spaces and , respectively. If and have isomorphic basic subspaces and if the quotient spaces and are isomorphic, there exists an isomorphism from onto that maps onto and induces the given isomorphism on the quotient spaces. In particular, and are isomorphic.

**[1]**R. Brown,*Valued vector spaces of countable dimension*, Publ. Math. Debrecen**18**(1971), 149-151. MR**0312202 (47:764)****[2]**L. Fuchs,*Vector spaces with valuations*, J. Algebra**35**(1975), 23-38. MR**0371995 (51:8212)****[3]**P. Hill,*Criteria for freeness in groups and valuated vector spaces*, Lecture Notes in Math., vol. 616, Springer-Verlag, Berlin and New York, 1977, pp. 140-157. MR**0486206 (58:5978)****[4]**P. Hill and E. White,*The projective dimension of valuated vector spaces*, J. Algebra**74**(1982), 374-401. MR**647246 (84d:18014)****[5]**F. Richman and E. Walker,*Valuated groups*, J. Algebra**56**(1979), 145-167. MR**527162 (80k:20053)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0702280-1

Keywords:
Valuated vector space,
basis,
nice subspace of free space (NSF-space),
isomorphism,
uniqueness theorem

Article copyright:
© Copyright 1983
American Mathematical Society