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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.19 no.2 Antofagasta Aug. 2000

http://dx.doi.org/10.4067/S0716-09172000000200002 

ON STRUCTURE AND COMMUTATIVITY OF NEAR - RINGS

H. A. S. ABUJABAL*, M.A. OBAID and M. A. KHAN
King Abdulaziz University, Saudi Arabia

AMS subject classification (1993): 16Y30, 16U80.

Key words: Near rings, D - near rings, distributively generated near rings, zero yummetric, zero commutative, commutativity, orthogonal sum and decomposition of near rings.

References

1. H.E. Bell, Certain near rings are rings. J. London Math. Soc., 4, pp. 264-270, (1971).         [ Links ]

2. H.E. Bell,  A. commutativity theorem for near rings, Canad. Math. Bull., 20, pp. 25-28, (1977).         [ Links ]

3. H.E. Bell, A. commutativity for rings, Canad. J. Math., 28, pp. 986-989, (1976).         [ Links ]

4. H.E. Bell and S. Ligh, Some decomposition theorems for periodic rings and near rings, Math. J. Okayama Univ., 31, pp. 93-99, (1989).         [ Links ]

5. J.R. Clay, The near rings on groups of low order, Math. Z., 104, pp. 364-371, (1968).         [ Links ]

6. J.R. Clay, Near rings, geneses and applications, Oxford Univ. Press, U.K. (1992).         [ Links ]

7. A. Frohlich, Distributively generated near rings, Proc. London Math. Soc., 8, pp. 76-94, (1958).         [ Links ]

8.- I.N. Herstein, A note on rings with central nilpotent elements, Proc. Amer. Math. Soc., 16, pp. 239-243, (1989).         [ Links ]

9. S. Ligh, On Boolean near - rings, Bull. Austral. Math. Soc., 1, pp.375-379, (1969).         [ Links ]

10. S. Ligh and J. Luh, Some commutativity theorems for rings and near - rings, Acta Math. Acad. Sci. Hungar., 28, pp. 19 - 23, (1976).         [ Links ]

11. S. Ligh and H. Luh, Direct sum of J. rings and zero rings, Amer. Math. Monthly, 96,  pp. 40-41 (1989).         [ Links ]

12. G. Pilz,Near - rings, (Second Edition), North - Holland, Mathematics Studies 23, Amsterdam, (1983).         [ Links ]

13. M.A. Quadri, M. Ashraf and A. Ali, Certain conditions under which near - rings are rings, Bull. Austral. Math. Soc., 42, pp. 91-94, (1990).         [ Links ]

Received: March, 1999.

H. A. S. Abujabal
M. A. Obaid

and

M. A. Khan
Department of Mathematics
Faculty of Science
King Abdulaziz University
P. O. Box 31464
Jeddah 21497
Saudi Arabia

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