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On ℵ0-categorical nilrings. II1

Published online by Cambridge University Press:  12 March 2014

Gregory Cherlin
Gregory Cherlin*
Affiliation:
Rutgers University, New Brunswick, New Jersey 08903
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Abstract

Theorem. The Jacobson radical of an ℵ0-categorical associative ring is nilpotent.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 45 , Issue 2 , June 1980 , pp. 291 - 301
Copyright
Copyright © Association for Symbolic Logic 1980

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Footnotes

1

I thank the German Academic Exchange Service (DAAD) for their support in June 1977. Research supported in part by NSF Grant MCS 76-06484.

References

REFERENCES

[1]Baldwin, J. and Rose, B., ℵ0-categoricity and stability of rings, Journal of Algebra, vol. 45 (1977), pp. 1–16.CrossRefGoogle Scholar
[2]Cherlin, G., On ℵ0-categorical nilrings (to appear).Google Scholar
[3]Jacobson, N., Structure of rings, American Mathematical Society, Providence, R.I., 1964.Google Scholar
[4]Kaplansky, I., Rings with a polynomial identity, Bulletin of the American Mathematical Society, vol. 54 (1948), pp. 447–459.CrossRefGoogle Scholar
[5]Macintyre, A. and Rosenstein, J., ℵ0-categoricity of rings without nilpotent elements and for Boolean structures, Journal of Algebra, vol. 43 (1976), pp. 129–154.CrossRefGoogle Scholar
[6]Procesi, C., PI rings, Marcel Dekker, New York, 1973.Google Scholar
[7]Rose, B., Model theory of alternative rings, Notre Dame Journal of Format Logic, vol. 19 (1978), p. 238.Google Scholar
[8]Rosenstein, J., ℵ0-categoricity of groups, Journal of Algebra, vol. 25 (1973), pp. 435–467.CrossRefGoogle Scholar