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Theories of modules closed under direct products

Published online by Cambridge University Press:  12 March 2014

Roger Villemaire
Roger Villemaire*
Affiliation:
Département de Mathématiques et Informatique, Université du Québec à Montréal, Montréal, Québec H3C 3P8, Canada, E-mail: villem@math.uqam.ca
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Abstract

We generalize to theories of modules (complete or not) a result of U. Felgner stating that a complete theory of abelian groups is a Horn theory if and only if it is closed under products. To prove this we show that a reduced product of modules ΠFMi (i ϵ I) is elementarily equivalent to a direct product of ultraproducts of the modules Mi(i ϵ I).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 2 , June 1992 , pp. 515 - 521
Copyright
Copyright © Association for Symbolic Logic 1992

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References

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