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A note on the independence of the axioms for a vector space

Published online by Cambridge University Press:  09 April 2009

A. J. Van Der Poorten
A. J. Van Der Poorten
Affiliation:
University of New South Wales
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It is customary to define a vector space in some such manner as: A vector space over a field F is a set V of elements a, b, … called vectors, having the following properties: For arbitrary a, b, c ∈ V; λ, μ ∈ F.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 4 , November 1967 , pp. 425 - 428
Copyright
Copyright © Australian Mathematical Society 1967

References

[1]Clifford, A. H. and Preston, G. B., The algebraic theory of semi-groups (Mathematical Surveys Number 7, Amer. Math. Soc., 1961).Google Scholar
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[4]Huntington, E. V., ‘Simplified definition of a group’ Bull. Amer. Math. Soc. 8 (1901–1902), 296–300.CrossRefGoogle Scholar