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A characterization of semi-prime ideals in near-rings

  • N. J. Groenewald (a1)

Abstract

It is well-known that in any near-ring, any intersection of prime ideals is a semi-prime ideal. The aim of this note is to prove that any ideal is a prime ideal if and only if it is equal to its prime radical. As a consequence of this we have any semi-prime ideal I in a near-ring N is the intersection of minimal prime ideals of I in N and that I is the intersection of all prime ideals containing I.

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Copyright

References

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[1]Pilz, G. (1977), Near-rings (North-Holland, Amsterdam-New York).
[2]Rao, V. Sambasiva, ‘A characterization of semi-prime ideals in near-rings’, J. Austral. Math. Soc. Ser. A 32 (1982), 212214.
[3]Van der Walt, A. P. J., ‘Prime ideals and nil radicals in near-rings’, Arch. Math. (Basel) 15 (1964), 408414.
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