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Hereditariness of strong and stable radicals

Published online by Cambridge University Press:  18 May 2009

E. R. Puczyłowski
E. R. Puczyłowski
Affiliation:
Institute of Mathematics, University of Warsaw, Pkin, 00–901 Warsaw
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The aim of this paper is to discuss some relations among hereditary, strong and stable radicals. In particular we investigate hereditariness of lower strong and stable radicals. Some facts obtained are related to some results and questions of [2, 6, 7].

All rings in the paper are associative. Fundamental definitions and properties of radicals may be found in [9]. Definitions of hereditary and strong radicals are used as in Sands [7]. We say that a radical S is left (right) stable if

(ρ): for every ring R and every left (right) ideal I of R it follows S(I)⊆S(R).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 23 , Issue 1 , January 1982 , pp. 85 - 90
Copyright
Copyright © Glasgow Mathematical Journal Trust 1982

References

REFERENCES

1.Divinsky, N., Krempa, J. and Suliński, A., Strong radical properties of alternative and associative rings, J. Algebra 17 (1971), 369–388.CrossRefGoogle Scholar
2.Jaegerman, M. and Sands, A. D., On normal radicals, N-radicals and A-radicals, J. Algebra 50 (1978), 337–349.CrossRefGoogle Scholar
3.Puczyłowski, E. R., On lower strong radicals in alternative algebras, Bull. Acad. Polon. Sci. 25 (1977), 617–622.Google Scholar
4.Puczyłowski, E. R., Remarks on stable radicals, Bull. Acad. Polon. Sci. 28 (1980), 11–16.Google Scholar
5.Rossa, R. F. and Tangeman, R. L., General hereditary for radical theory, Proc. Edinburgh Math. Soc. 20 (1977), 333–337.CrossRefGoogle Scholar
6.Sands, A. D., On normal radicals, J. London Math. Soc. 11 (1975), 361–365.CrossRefGoogle Scholar
7.Sands, A. D., On relations among radical properties, Glasgow Math. J. 18 (1977), 17–23.CrossRefGoogle Scholar
8.Stewart, P. N., Strict radical classes of associative rings, Proc. Amer. Math. Soc. 39 (1973), 273–278.CrossRefGoogle Scholar
9.Wiegandt, R., Radical and semisimple classes of rings (Ontario, 1974).Google Scholar