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Strongly Prime Near-Ring Modules

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Abstract

We introduce the notion of a strongly prime near-ring module and then characterize strongly prime near-rings in terms of strongly prime modules. Furthermore, we define a \({\mathcal{T}}\)-special class of near-ring modules and then show that the class of strongly prime modules forms a \({\mathcal{T}}\)-special class. \({\mathcal{T}}\)-special classes of strongly prime modules are then used to describe the strongly prime radical.

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References

  1. Andrunakievich, V.A.: Radicals in associative rings I, Math Sbornik, 44 (1958), 179–212 (in Russian); English translation in Am. Math. Soc. Transl. 52, 95–128 (1966)

  2. Andrunakivic, V.A.; Rjabuhin, J.M.: Modules and Radicals Dokl.Akad. Nauk SSSR. Matem. 156 (1964), 991–994 (in Russian) English translation in Soviet Maths. Doklady 5, 728–732

  3. Beachy J.A.: Some aspects of non-commutative localization. Non-commutative ring theory, Springer-Verlag Lecture Notes 545, 2–31 (1975)

    MathSciNet  Google Scholar 

  4. Birkenmeier G.F., Heatherly H., Lee E.: An Andrunakievich lemma for near-rings. Comm. Algebra 23, 2825–2850 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  5. De La Rosa B., Veldsman S.: A relationship between ring radicals and module radicals. Quaestiones Mathematicae 17, 453–467 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  6. Divinsky N.: Rings and Radicals. University Toronto Press, Ontario (1965)

    MATH  Google Scholar 

  7. Groenewald N.J.: Strongly prime near-rings. Proc. Edinb. Math. Soc. 31, 337–343 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  8. Groenewald N.J.: Strongly prime near-rings 2. Comm. Algebra 17, 735–749 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  9. Groenewald, N.J.; Juglal, S.; Lee, E.K.S.: Different prime R-ideals. Algebra Colloquium, 17(Spec 1), 887–904 (2010)

    Google Scholar 

  10. Kaarli, K.: Survey on the radical theory of near-rings. Contributions to General Algebra 4 (Teubner, Stuttgart, 1987), 45–62

  11. Handelman D., Lawrence J.: Strongly prime rings. Trans. Am. Math. Soc. 211, 209–223 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  12. Nicholson W.K., Watters J.F.: The strongly prime radical. Proc. Am. Math. Soc. 76, 235–239 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  13. Pilz, G.: Near-Rings (revised edition), North-Holland, Amsterdam (1983)

  14. Veldsman S.: On the characterization of overnilpotent radical classes of near-rings by N-groups. South Afr. J. Sci. 87, 215–216 (1991)

    Google Scholar 

  15. Szasz F.A.: Radicals of Rings. Wiley, New York (1981)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, Nelson Mandela Metropolitan University, P O Box 77000, Port Elizabeth, 6031, South Africa

    S. Juglal & N. J. Groenewald

Authors
  1. S. Juglal
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  2. N. J. Groenewald
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Correspondence to N. J. Groenewald.

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Juglal, S., Groenewald, N.J. Strongly Prime Near-Ring Modules. Arab J Sci Eng 36, 985–995 (2011). https://doi.org/10.1007/s13369-011-0092-2

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  • DOI: https://doi.org/10.1007/s13369-011-0092-2

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