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QE rings in characteristic pn

Published online by Cambridge University Press:  12 March 2014

Chantal Berline  and
Gregory Cherlin
Chantal Berline
Affiliation:
University of Paris 7, Paris, France
Gregory Cherlin
Affiliation:
Rutgers University, New Brunswick, New Jersey 08903
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Abstract

We show that all QE rings of prime power characteristic are constructed in a straightforward way out of three components: a filtered Boolean power of a finite field, a nilpotent Jacobson radical, and the ring Zp. or the Witt ring W2(F4) (which is the characteristic four analogue of the Galois field with four elements).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 48 , Issue 1 , March 1983 , pp. 140 - 162
Copyright
Copyright © Association for Symbolic Logic 1983

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References

REFERENCES

[1]Berline, Ch., Rings which admit elimination of quantifiers, this Journal, vol. 46 (1981), pp. 56–58.Google Scholar
[2]Berline, Ch. and Cherlin, G., QE rings in characteristic p, Proceedings of the Storrs Conference (to appear).Google Scholar
[3]Berline, Ch. and Cherlin, G., QE nilrings of prime characteristic, Proceedings of the Logic Meeting in Brussels and Mons (to appear).Google Scholar
[4]Boffa, M., Macintyre, A. and Point, F., The quantifier elimination problem for rings without nilpotent elements and for semi-simple rings, Proceedings of the 4th Bierutowice Conference (to appear).Google Scholar
[5]Chevalley, C., Démonstration d'une hypothèse de M. Artin, Abhandlungen aus dent Mathematischen Seminar der Hansischen Unirersität, vol. 11, Leipzig, 1936, pp. 73–75.Google Scholar
[6]Jacobson, N., Structure of rings, Amer. Math. Soc., Vol. 37, Providence, 1964.Google Scholar
[7]Macintyre, A., On ℵ1-categorical theories of fields, Fundamenta Mathematicae, vol. 71 (1971), pp. 1–25.CrossRefGoogle Scholar
[8]Macintyre, A. and Rosenstein, J.G., ℵ0-categoricity for rings without nilpotent elements and for Boolean structures, Journal of Algebra, vol. 43 (1976), pp. 129–145.CrossRefGoogle Scholar
[9]Rose, B., Rings which admit elimination of quantifiers, this Journal, vol. 43 (1978), pp. 92–112; Corrigendum, this Journal, vol. 44 (1979), pp. 109–110.Google Scholar