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 | 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]**Ron Brown,*Valued vector spaces of countable dimension*, Publ. Math. Debrecen**18**(1971), 149–151 (1972). MR**0312202****[2]**L. Fuchs,*Vector spaces with valuations*, J. Algebra**35**(1975), 23–38. MR**0371995****[3]**Paul Hill,*Criteria for freeness in groups and valuated vector spaces*, Abelian group theory (Proc. Second New Mexico State Univ. Conf., Las Cruces, N.M., 1976) Springer, Berlin, 1977, pp. 140–157. Lecture Notes in Math., Vol. 616. MR**0486206****[4]**Paul Hill and Errin White,*The projective dimension of valuated vector spaces*, J. Algebra**74**(1982), no. 2, 374–401. MR**647246**, 10.1016/0021-8693(82)90031-X**[5]**Fred Richman and Elbert A. Walker,*Valuated groups*, J. Algebra**56**(1979), no. 1, 145–167. MR**527162**, 10.1016/0021-8693(79)90330-2

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Additional Information

DOI:
http://dx.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