PROPERTIES ON TYPES OF PRIMITIVE NEAR-RINGS Cho, Yong-Uk;
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.
simple;R-simple;monogenic;strongly monogenic;faith-ful R-groups;D.G. (R, S)-group;3 types of R-groups;modular right ideals;t-modular right ideals and 3 types of primitive near-rings;
F. W. Anderson and K. R. Fuller, Rings and categories of modules, SpringerVerlag, New York, Heidelberg, Berlin, 1974.
G. Betsch, Primitive near-rings, Math. Z. 130 (1973), 351-361.
Y. U. Cho, On faithful monogenic R-groups and related substructures, J. of Natural Science Institute at Silla Univ. 11 (2002), 27-43.
K. Kaarli, Primitivity and simplicity of non-zero symmetric near-rings, Comm. Algebra 26(11) (1998), 3691-3708.
C. G. Lyons and J. D. P. Meldrum, Characterizing series for faithful D.G. near-rings, Proc. Amer. Math. Soc. 72 (1978), 221-227.
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.
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.
J. D. P. Meldrum, Upper faithful D.G. near-rings, Proc. Edinburgh Math. Soc. 26 (1983), 361-370.
J. D. P. Meldrum, Near-rings and their links with groups, Pitman Advanced Publishing Program, Boston, London, Melbourne, 1985.
G. Pilz, Near-rings, North Holland Publishing Company, Amsterdam, New York, Oxford, 1983.