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A remark on Ribenboim's paper ‘On the extension of orders in ordered modules’

Published online by Cambridge University Press:  17 April 2009

D. Spoerel
D. Spoerel
Affiliation:
Mathematisches Seminar der Universität, Hamburg, Germany.
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Abstract

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We give another formulation of Theorem 1 of Ribenboim's paper, Bull. Austral. Math. Soc. 2 (1970), 81–88. Our condition on a module to be totally ordered such that this order extends a given strict order seems to be more useful for applications than condition (2) of Ribenboim. This is shown for example in Corollaries 3 and It of our paper. Corollary 4 is due to Ribenboim. Corollary 3 generalizes the corresponding well known result on abelian groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 6 , Issue 2 , April 1972 , pp. 251 - 253
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Ribenboim, P., “On the extension of orders in ordered modules”, Bull. Austral. Math. Soc. 2 (1970), 81–88.CrossRefGoogle Scholar