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Logic Journal of IGPL Advance Access originally published online on August 6, 2007
Logic Journal of IGPL 2008 16(1):99-102; doi:10.1093/jigpal/jzm029
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

An Application of Model Theory to Semimodules

M. Zayed

University of Banha, Faculty of Science, Departement of Mathematics, Banha 13518 - Egypt. E-mail: maherzayed{at}hotmail.com


  Abstract

In this note, we prove that the theory T of cancellative semimodules over a semiring R has the amalgamation property. If R is an entire cancellative zerosumfree semiring, then T has no model-companion. In particular, the theory of commutative additively cancellative monoids forms an example of a non-companionable theory.


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