Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

PROPERTIES ON TYPES OF PRIMITIVE NEAR-RINGS

  • Cho, Yong-Uk (Department of Mathematics College of Natural Sciences Silla University)
  • Published : 2004.10.01
Download PDF
⟨ Previous Next ⟩

Abstract

Throughout this paper, we will consider that R is a near-ring and G an R-group. We initiate the study of monogenic, strongly monogenic R-groups, 3 types of nonzero R-groups and their basic properties. At first, we investigate some properties of D.G. (R, S)-groups, faithful R-groups, monogenic R-groups, simple and R-simple R-groups. Next, we introduce modular right ideals, t-modular right ideals and 3 types of primitive near-rings. The purpose of this paper is to investigate some properties of primitive types near-rings and their characterizations.

Keywords

References

  1. F. W. Anderson and K. R. Fuller, Rings and categories of modules, SpringerVerlag, New York, Heidelberg, Berlin, 1974.
  2. G. Betsch, Primitive near-rings, Math. Z. 130 (1973), 351-361. https://doi.org/10.1007/BF01179162
  3. Y. U. Cho, On faithful monogenic R-groups and related substructures, J. of Natural Science Institute at Silla Univ. 11 (2002), 27-43.
  4. K. Kaarli, Primitivity and simplicity of non-zero symmetric near-rings, Comm. Algebra 26(11) (1998), 3691-3708. https://doi.org/10.1080/00927879808826367
  5. C. G. Lyons and J. D. P. Meldrum, Characterizing series for faithful D.G. near-rings, Proc. Amer. Math. Soc. 72 (1978), 221-227. https://doi.org/10.1090/S0002-9939-1978-0507312-X
  6. S. J. Mahmood and J. D. P. Meldrum, D.G. near-rings on the infinite dihedral groups, Near-rings and Near-fieds (1987), Elsevier Science Publishers B.V.(North-Holland), 151-166. https://doi.org/10.1016/S0304-0208(08)72298-9
  7. C. J. Maxson and A. B. Van der Merwe, Forcing linearity numbers for modules over rings with nontrivial idempotents, J. Algebra 256 (2002), Academic Press, 66-84. https://doi.org/10.1016/S0021-8693(02)00128-X
  8. J. D. P. Meldrum, Upper faithful D.G. near-rings, Proc. Edinburgh Math. Soc. 26 (1983), 361-370. https://doi.org/10.1017/S0013091500004430
  9. J. D. P. Meldrum, Near-rings and their links with groups, Pitman Advanced Publishing Program, Boston, London, Melbourne, 1985.
  10. G. Pilz, Near-rings, North Holland Publishing Company, Amsterdam, New York, Oxford, 1983.