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On radicals of finite near-rings

Published online by Cambridge University Press:  20 January 2009

K. Kaarli
K. Kaarli
Affiliation:
Department of Mathematics, Tartu State UniversityTartu, Estonia, USSR
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Abstract

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In this paper the study of radicals of finite near-rings is initiated. The main result (Theorem 4.3) gives a description of hereditary radicals having hereditary semisimple classes too. Also it is shown that there exist non-hereditary radicals having hereditary semisimple classes.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 27 , Issue 3 , October 1984 , pp. 247 - 259
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

REFERENCES

1.Betsch, G., Ein radikal fur fastringe, Math. Z. 78 (1962), 86–90.CrossRefGoogle Scholar
2.Betsch, G. and Kaarli, K., Supernilpotent radicals and hereditariness of semisimple classes of near-rings, Radical Theory (Proc. Conf. Eger, 1982, Colloq. Math. Soc. J. Bolyai, North-Holland, Amsterdam), to appear.Google Scholar
3.Betsch, G. and Wiegandt, R.Non-hereditary semisimple classes of near-rings, Studia Sci. Math Hungar. 17 (1982), 69–75.Google Scholar
4.Blackett, D. W., Simple and semisimple near-rings, Proc. Amer. Math. Soc. 4 (1953), 772–785.CrossRefGoogle Scholar
5.Fisher, J. L., Radicals for finite rings, manuscript.Google Scholar
6.Fisher, J. L., Radicals of rings with composition series, manuscript.Google Scholar
7.Gardner, B. J.Some degeneracy and pathology in non-associative radical theory, Annales Univ. Sci. Budapest Sect. Math. 22–23 (1979–1980), 65–74.Google Scholar
8.Kaarli, K.Minimal ideals of near-rings, Tartu Riikl. Ül. Toimetised, Vih. 366 (1975), 105–142 (in Russian).Google Scholar
9.Kaarli, K., Radicals of near-rings, Tartu Riikl. Ül. Toimetised, Vih. 390 (1976), 134–171 (in Russian).Google Scholar
10.Kaarli, K.The classification of irreducible R-groups over a semiprimary near-ring, Tartu Riikl. Ül. Toimetised, Vih. 556 (1981), 47–63 (in Russian).Google Scholar
11.Pilz, G.Near-rings (North-Holland, Amsterdam, 1977).Google Scholar
12.Polin, S. V.Primitive m-near-rings over multi-operator groups, Math. Sbornik 13 (1971), 247–265 (in Russian).CrossRefGoogle Scholar
13.Polin, S. V.Radicals in MΩ-near-rings II, Izv. Vysš. Učebn. Zaved. Mathematika 2 (1972), 63–71 (in Russian).Google Scholar
14.Widiger, A. and Wiegandt, R.Theory of radicals for hereditarily artinian rings, Acta Sci. Math. 39 (1977), 303–312.Google Scholar