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On Left Bipotent Near-Rings

Published online by Cambridge University Press:  20 January 2009

J. L. Jat  and
S. C. Choudhary
J. L. Jat
Affiliation:
Department of Mathematics, SBSH, University of UdaipurUdaipur-313001, India
S. C. Choudhary
Affiliation:
Department of Mathematics, SBSH, University of UdaipurUdaipur-313001, India
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A near-ring N is defined to be left bipotent if Na = Na2 for each a in N. Many properties of such near-rings are proved in Section 1, and results of Chandran (4) are generalised. Most of the results are different from, and contrary to, the ring case. Necessary and sufficient conditions have also been obtained under which such near-rings become regular. Section 2 deals with left bipotent near-rings without zero divisors. Some structure theorems for direct sum decompositions and J(N) = (0) are proved and it is shown that for a left bipotent S-near-ring, the singular ‘set’ S(N) = 0. Necessary examples and counter examples are supplied.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 2 , June 1979 , pp. 99 - 107
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

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