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PROPERTIES ON TYPES OF PRIMITIVE NEAR-RINGS

Cho, Yong-Uk    (Department of Mathematics College of Natural Sciences Silla University  );
  • 초록

    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.


  • 주제어

    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.  

  • 참고문헌 (10)

    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. 
    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. 
    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. 
    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. 
    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. 
    8. J. D. P. Meldrum, Upper faithful D.G. near-rings, Proc. Edinburgh Math. Soc. 26 (1983), 361-370. 
    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. 

 저자의 다른 논문

  • Cho, Yong-Uk (47)

    1. 1998 "A STUDY ON D.G. NEAR-RINGS AND THEIR MODULES" East Asian mathematical journal 14 (1): 135~140    
    2. 1999 "ON STRONG REGULARITY AND STRONG REDUCIBILITY OF NEAR-RINGS" East Asian mathematical journal 15 (2): 247~253    
    3. 2000 "SOME PROPERTIES ON DERIVATION IN NEAR-RINGS" East Asian mathematical journal 16 (2): 355~361    
    4. 2000 "A Characterization on Strong Reducibility of Near-Rings" 한국수학교육학회지. 시리즈 E: 수학교육논문집 10 (): 283~292    
    5. 2001 "A NOTE ON D.G. NEAR-RING GROUPS" East Asian mathematical journal 17 (2): 287~295    
    6. 2001 "A STUDY ON ANNIHILATOR CONDITIONS OF POLYNOMIALS" Bulletin of the Korean Mathematical Society = 대한수학회보 38 (1): 137~142    
    7. 2001 "A STUDY ON ADDITIVE ENDOMORPHISMS OF RINGS" Bulletin of the Korean Mathematical Society = 대한수학회보 38 (1): 149~156    
    8. 2001 "SOME CONDITIONS ON DERIVATIONS IN PRIME NEAR-RINGS" Journal of the Korean Society of Mathematical Education. 한국수학교육학회지. Series B, Pure and applied mathematics 8 (2): 145~152    
    9. 2002 "RINGS WHOSE ADDITIVE MAPPINGS ARE GENERATED BY MULTIPLICATIVE AND RELATED RINGS" East Asian mathematical journal 18 (1): 51~58    
    10. 2002 "ON AGE RINGS AND AM MODULES WITH RELATED CONCEPTS" East Asian mathematical journal 18 (2): 245~259    

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