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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

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