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On quasi-regularity in gamma near-rings

  • Srinivasa Rao Ravi
  • Krishnaveni Cheruvu
Original Paper
  • 11 Downloads

Abstract

The Jacobson radicals, \(J_\nu \), (\(\nu = 0, 1, 2\)), of \(\Gamma \)-near-rings were introduced and studied by Booth. In this paper quasi-regular elements in a \(\Gamma \)-near-ring are introduced and a characterization of the \(J_0\)-radical of a \(\Gamma \)-near-ring in terms of quasi-regular ideals is given. It is also proved that \(J_0(M)\) is nilpotent for a \(\Gamma \)-near-ring M with DCC on \(M\Gamma \)-subgroups of M. It is verified that if M is a \(\Gamma \)-near-ring satisfying DCC on \(M \Gamma \)-subgroups of M then \(J_{2}(M) = J_{1}(M) = J_{1/2}(M) = J_{0}(M)\).

Keywords

Gamma near-ring Quasi-regular elements Modular left ideals of type-0, 1 and 2 Jacobson radicals of type-0, 1 and 2 

Mathematics Subject Classification

16Y30 

Notes

Acknowledgements

This work is done under the UGC sponsored minor research project, MRP-2345/06 (UGC-SERO), Dt.10.01.2007. The second author would like to thank the management of Maris Stella College, Vijayawada, A.P., India, for providing her with the necessary facilities.

References

  1. Booth, G.L.: A note on \(\Gamma \)-near-rings. Stud. Sci. Math. Hung. 23, 471–473 (1998)MathSciNetGoogle Scholar
  2. Booth, G.L.: Jacobson radicals of \(\Gamma \)-near-rings. In: rings, modules and radicals (Hobart, 1987) 1–12, (Pitman research notes, Math. Ser. 204), Longman Sci. Tech., Harlow (1989)Google Scholar
  3. Pilz, G.: Near-rings, revised edn. North-Holland, Amsterdam (1983)Google Scholar

Copyright information

© The Managing Editors 2018

Authors and Affiliations

  1. 1.Department of MathematicsR. V. R. & J. C. College of EngineeringGunturIndia
  2. 2.Department of MathematicsMaris Stella CollegeVijayawadaIndia

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