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

Quotients of valuated vector spaces


Author: Paul Hill
Journal: Proc. Amer. Math. Soc. 81 (1981), 14-18
MSC: Primary 18G05; Secondary 15A03, 18G20, 20K10
MathSciNet review: 589128
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Abstract: This paper has three purposes. The first is to present a direct example of a quotient of an injective space that is not itself injective. The second is to demonstrate that Theorem 3 in [2] is false. An $ s$-dense subspace $ S$ of a free space $ F$ is not free by virtue of $ F/S$ having only values that are cofinal with $ \omega $. Finally, we furnish a valid proof, independent of the aforementioned Theorem 3, that a subspace $ V$ of a free space is free if $ V$ satisfies Fuchs' countability condition.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0589128-1
PII: S 0002-9939(1981)0589128-1
Keywords: Valuation, valuated vector space, free space, quotient of injective, $ s$-dense subspace, separable subspace, projective dimension greater than one, criterion for freeness
Article copyright: © Copyright 1981 American Mathematical Society