Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-26T13:50:18.417Z Has data issue: false hasContentIssue false
  • English
  • Français

Dual modules

Published online by Cambridge University Press:  24 October 2008

W. J. R. Mitchell
W. J. R. Mitchell
Affiliation:
Magdalene College, Cambridge
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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