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ON NEAR-RINGS WITH STRONG REGULARITY

Cho, Yong-Uk    (DEPARTMENT OF MATHEMATICS, SILLA UNIVERSITY  );
  • 초록

    Throught this paper, we will investigate some properties of left regular and strongly reduced near-rings. Mason introduced the notion of left regularity and he characterized left regular zero-symmetric unital near-rings. Also, this concept have been studied by several authors. The purpose of this paper is to find some characterizations of the strong reducibility in near-rings, and the strong regularity in near-rings which are closely related with strongly reduced near-rings.


  • 주제어

    left regular .   right regular .   strongly regular .   strongly right regular .   left $\kappa$-regular .   strongly reduced and left semi-central.  

  • 참고문헌 (6)

    1. Cho, Y.: Near-rings with left Baer like conditions. Bull. Korean Math. Soc. 45 (2008), no. 2, 263-267.     
    2. Cho, Y.: Characterizations of left regularity. Far East J. Math. Soc., to appear. 
    3. Mason, G.: A note on strong forms of regularity for near-rings. Indian J. Math. 40 (1998), no. 2, 149-153. 
    4. Murty, C. V. L. N.: Generalized near-fields. Proc. Edinburgh Math. Soc. 27 (1984), 21-24. 
    5. Pilz, G.: Near-Rings. North-Holland Publishing Company, Amsterdam, New York, Ox-ford, 1983. 
    6. Reddy, Y.V. & Murty, C. V. L. N.: On strongly regular near-rings. Proc. Edinburgh Math. Soc. 27 (1984), 61-64. 

 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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