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A short algebraic proof of a theorem of Warfield

Published online by Cambridge University Press:  26 February 2010

A. Laradji
A. Laradji
Affiliation:
Department of Mathematical Sciences, K.F.U.P.M., Dhahran 31261, Saudi Arabia.
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Abstract

In this note we give a direct algebraic proof of a theorem of Warfield on algebraically compact modules. It is shorter than the one given by Azumaya in [1], in that it does not use the embedding of a module M into M** (where M* is the character Homz (M, Q/Z)).

Type
Research Article
Information
Mathematika , Volume 40 , Issue 2 , December 1993 , pp. 275 - 277
Copyright
Copyright © University College London 1993

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References

1.Azumaya, G.. An algebraic proof of a theorem of Warfield on algebraically compact modules. Math. J. Okayama Univ., 28 (1986), 53–60.Google Scholar
2.Laradji, A.. Compactness in Modules. Ph.D Thesis (Sheffield University, 1985).Google Scholar
3.Warfield, R. B. Jr. Purity and algebraic compactness for modules. Pacific J. Math., 28 (1969), [ILL]–719.CrossRefGoogle Scholar