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Dual modules

Published online by Cambridge University Press:  24 October 2008

W. J. R. Mitchell
W. J. R. Mitchell
Affiliation:
Magdalene College, Cambridge
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Extract

Introduction and statement of results. It is well known that if V is a vector space over a field k then its dual vector space Homk (V, k) has dimension not less than that of V, and that the dimensions are equal precisely when V is finite-dimensional. In this note we introduce a ‘dual module’ for a module over a principal ideal domain, and show that some though not all of the properties of the field case carry over.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 1 , July 1978 , pp. 21 - 24
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

(1)Beyl, F. R. and Hanna, A.Ext (−, )-reproduced Abelian groups are finite. Acta Math. 28 (1976), 267–269.Google Scholar
(2)Chase, S. U.Locally free modules and a problem of Whitehead. Illinois J. Math. 6 (1962), 682–689.Google Scholar
(3)Fuchs, L.Infinite Abelian groups, vols. 1 and 2 (Academic Press, 1971, 1973).Google Scholar
(4)Lacher, R. C.Cell-like mappings and their generalisations. Bull. Amer. Math. Soc. 83 (1977), 495–553.CrossRefGoogle Scholar
(5)Nunke, R. J. and Rotman, J.Singular cohomology groups. J. London Math. Soc. 37 (1962), 301–306.CrossRefGoogle Scholar