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On accessible subrings of associative rings

Published online by Cambridge University Press:  20 January 2009

R. R. Andruszkiewicz
R. R. Andruszkiewicz
Affiliation:
Institute of MathematicsUniversity of WarsawBialystok DivisionAkademicka 215–267 Bialystok, Poland
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We describe for every natural n the class of rings R such that if R is an accessible (left accessible) subring of a ring then R is an n-accessible (n-left-accessible) subring of the ring. This is connected with the problem of the termination of Kurosh's construction of the lower (lower strong) radical. The result for n = 2 was obtained by Sands in a connection with some other questions.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 1 , February 1992 , pp. 101 - 107
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

REFERENCES

1.Beidar, K. I., A chain of Kurosh may have an arbitrary finite length, Czechoslovak Math. J. 32, (1982), 418–422.CrossRefGoogle Scholar
2.Heinicke, A., A note on lower radical constructions for associative rings, Canad. Math. Bull. 11 (1968), 23–30.CrossRefGoogle Scholar
3.Xue, Liu Shao, Lun, Luo Yun, Ping, Tang Ai, Jie, Xiao and Yun, Guo Jin, Some results on modules and rings, Bull. Soc. Math. Belg. Sér. B 39 (1987), 181–193.Google Scholar
4.L'vov, I. V., Sidorow, A. V., Stabilization of Kurosh chains, Mat. Zametki 36 (1984), 815–821 (in Russian).Google Scholar
5.Puczylowski, E. R., On a question concerning strong radicals of associative rings, Quaestiones Math. 10 (1987), 321–338.CrossRefGoogle Scholar
6.Sands, A. D., On ideals in over-rings, Publ. Math. Debrecen 35 (1988), 273–279.CrossRefGoogle Scholar
7.Sands, A. D., Radicals and one-sided ideals, Proc. Roy. Soc. Edinburgh Sect. A 103 (1986), 241–251.CrossRefGoogle Scholar
8.Sulinski, A., Anderson, T. and Divinsky, N., Lower radical properties of associative and alternative rings, J. London Math. Soc. 41 (1966), 417–424.CrossRefGoogle Scholar
9.Waiters, J. F., On the lower radical construction for algebras, preprint.Google Scholar