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On the Homological Dimension of Valuated Vector Spaces

Published online by Cambridge University Press:  20 November 2018

Errin Erb White*
Affiliation:
Department of Mathematics, Auburn University, Auburn, Alabama 36830
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Following L. Fuchs [1], we define a valuated vector space to be a vector space V with a valuation from V to a totally ordered set Γ in which every nonempty subset has a supremum. It is assumed that Γ has a maximum element . A standard model for Γ is a closed initial segment of ordinals with the symbol ∞ adjoined.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Fuchs, L., “Vector spaces with valuations”, J. Algebra 35 (1962), 23-38. M.R. #8212.Google Scholar
2. Fuchs, L., and Irwin, J. M., On pω+i-projective p-groups, Proc. London Math. Soc. (3) 30 (1962), 459-470.Google Scholar
3. Hill, P., “Criteria for freeness in groups and valuated vector spaces”, Abelian group theory, Lecture Notes in Mathematics, Vol. 616, Springer-Verlag, Berlin, Heidelberg, New York, 1977, pp. 140-157.Google Scholar
4. Northcott, D. G., An introduction to homological algebra, Cambridge University Press, New York, 1960. M. R. #9523.Google Scholar
5. Richman, F. and Walker, E. A., Valuated groups, Journal of Algebra, 56 (1), (1962), 145-167.Google Scholar