Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-28T07:13:36.627Z Has data issue: false hasContentIssue false
  • English
  • Français

On left strong radicals of near-rings

Published online by Cambridge University Press:  13 July 2011

T. Anderson ,
K. Kaarli  and
R. Wiegandt
T. Anderson
Affiliation:
10072, 276 StreetWhonnock, B.C., V0M 1SO, Canada
K. Kaarli
Affiliation:
Department of Algebra and GeometryTartu State UniversityTartu, Estonia, Soviet Union
R. Wiegandt
Affiliation:
Mathematical InstituteHungarian Academy of SciencesP.O. Box 127H-1364 Budapest
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we shall deal with radicals γ of near-rings such that for every near-ring N its radical γ(N) contains all left ideals (left invariant subgroups, respectively) I of N with I∈γ. At first, examples of such radicals will be given. Then we shall prove that these radicals are hypersolvable and have hereditary semisimple classes.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 3 , October 1988 , pp. 447 - 456
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCES

1.Anderson, T., Kaarli, K. and Wieoandt, R., Radical and subdirect decompositions, Comm. Algebra 13 (1985), 479–494.CrossRefGoogle Scholar
2.Betsch, G. and Kaarli, K., Supernilpotent radicals and hereditariness of semisimple classes of near-rings, Coll. Math. Soc. J. Bolyai 38 (Radical Theory, Eger, 1982, North-Holland, 1985) 47–58.Google Scholar
3.Holcombe, M., A hereditary radical for near-rings, Studia Sci. Math. Hungar. 17 (1982), 453–456.Google Scholar
4.Holcombe, M. and Walker, R., Radicals in categories, Proc. Edinburgh Math. Soc. 21 (1978/1979), 111–128.CrossRefGoogle Scholar
5.Kaarli, K., Minimal ideals in near-rings, Tartu Riikl. Ül. Toimetised 366 (1975), 105–142 (in Russian).Google Scholar
6.Kaarli, K., Radicals in near-rings, Tartu Riikl. Ul. Toimetised 390 (1976), 134–171 (in Russian).Google Scholar
7.Kaarli, K., Classification of irreducible R-groups over a semiprimary near-ring, Tartu Riikl. Ül. Toimetised 556 (1981), 47–63 (in Russian).Google Scholar
8.Mlitz, R. and Oswald, A., Hypersolvable and Supernilpotent radicals, Studio Sci. Math. Hungar. 24 (1989), to appear.Google Scholar
9.Pilz, G., Near-rings (North-Holland, 1977).Google Scholar
10.Polin, S. V., Radicals in mΩ-rings, II, Izv. Vyssh. Vchebn. Zaved. Mat. 117 (1972), 63–71 (in Russian).Google Scholar
11.Ramakotaiah, D., Structure of 1-primitive near-rings, Math. Z. 110 (1969), 15–26.CrossRefGoogle Scholar
12.Wiegandt, R., Radical and Semisimple Classes of Rings (Queen's Papers in Pure and Appl. Math. 37, Kingston, Ontario, 1974).Google Scholar
13.Wiegandt, R., Semisimple classes and H-relations, Studia Sci. Math. Hungar. 13 (1978), 181–185.Google Scholar