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Primitive near-rings do not form an axiomatisable class

Published online by Cambridge University Press:  14 November 2011

Maher Zayed
Maher Zayed
Affiliation:
Department of Mathematics, University of Bahrain, PO Box 32038, Isa Town, State of Bahrain
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Synopsis

It is shown that for each v ∊ {0, 1, 2}, the class of v-primitive near-rings is not axiomatisable.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 2 , 1993 , pp. 399 - 400
Copyright
Copyright © Royal Society of Edinburgh 1993

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References

1Chang, C. C. and Keisler, H. J.. Model theory (Amsterdam: North-Holland, 1977).Google Scholar
2Fuch, P. and Pilz, G.. Ultraproducts and ultra-limits of near-rings. Monatsh. Math. 100 (1985), 105–112.Google Scholar
3Lawrence, J. W.. Primitive rings do not form an elementary class. Comm. Algebra 9 (1981), 379–400.CrossRefGoogle Scholar
4Pilz, G.. Near-rings, 2nd edn. (Amsterdam: North Holland, 1983).Google Scholar