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A uniformly strongly prime radical

Published online by Cambridge University Press:  09 April 2009

D. M. Olson
Affiliation:
John Carroll University, University Heights, Ohio 44118, U.S.A.
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Abstract

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The class of all uniformly strongly prime rings is shown to be a special class of rings which generates a radical class which properly contains both the right and left strongly prime radicals and which is independent of the Jacobson and Brown-McCoy radicals.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Andrunakievič, V. A., ‘Radicals in associative rings I’, Amer. Math. Soc. Transl. Ser. 2 52 (1966), 95128.Google Scholar
[2]Divinsky, N., Rings and radicals (University of Toronto Press, Toronto, 1965).Google Scholar
[3]Goodearl, K. R., Handelman, D. and Lawrence, J., Strongly prime and completely torsion free rings (Carleton Mathematical Series No. 109, Carleton University, Ottowa 1974).Google Scholar
[4]Groenewald, N. J. and Heyman, G. A. P., ‘Certain classes of ideals in group rings II’, Comm. Algebra 9 (1981), 137148.CrossRefGoogle Scholar
[5]Handelman, D. and Lawrence, J., ‘Strongly prime rings’, Trans. Amer. Math. Soc. 211 (1975), 209223.CrossRefGoogle Scholar
[6]Heyman, G. A. P. and Roos, C., ‘Essential extensions in radical theory for rings’, J. Austral. Math. Soc. (Ser. A) 23 (1977), 340347.CrossRefGoogle Scholar
[7]Parmenter, M. M., Passman, D. S. and Stewart, P. N., ‘The strongly prime radical of crossed products’, Comm. Algebra 12(1984), 10991113.CrossRefGoogle Scholar
[8]Parmenter, M. M., Stewart, P. N. and Wiegandt, R., ‘On the Groenewald and Heyman strongly prime radical’, Quaestiones Math. 7 (1984), 225240.CrossRefGoogle Scholar
[9]Rubin, R. A., ‘Absolutely torsion free rings’, Pacific J. Math. 46 (1973), 503514.CrossRefGoogle Scholar