Abstract
It is shown that in the variety of all, not necessarily 0-symmetric near-rings, there are no non-trivial classes of near-rings which satisfy condition (F), no non-trivial (Kurosh-Amitsur) radical classes with the ADS-property and consequently no non-trivial ideal-hereditary radical classes. It is also shown that any hereditary semisimple class contains only 0-symmetric near-rings.
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References
Barua, M. N.,Near-rings and Near-ring modules — Some special types, PhD Thesis, Gauhati University, Assam, India.
Betsch, G. andKaarli, K.,Supernilpotent radicals and hereditariness of semismple classes of near-rings, Colloq. Math. Soc. János Bolyai38. North-Holland, Amsterdam, 1985, 47–58.
Kaarli, K.,On ideal transitivity in near-rings, Contrib. Gen. Algebra8. Hölder-Pichler-Tempsky, Vienna and Teubner, Stuttgart, 1992, 81–89.
Veldsman, S.,Modulo-constant ideal-hereditary radicals for near-rings, Quaest. Math.11 (1988), 253–278.
Veldsman, S.,On the non-hereditariness of radical and semisimple classes of near-rings, Studia Sci. Hungar.24 (1989), 315–323.
Veldsman, S.,Near-ring radicals with hereditary semsimple classes, Archiv Math.54 (1990), 443–447.
Veldsman, S.,An overnilpotent radical theory for near-rings, J. Algebra144 (1991), 248–265.
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AMS Subject Classification: 16Y30; 16N80.