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A characterization of semi-prime ideals in near-rings

Part of: Algebraic structures

Published online by Cambridge University Press:  09 April 2009

N. J. Groenewald
N. J. Groenewald
Affiliation:
Department of MathematicsUniversity of port Elizabeth6000 Port Elizabeth, South Africa
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Abstract

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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.

MSC classification

Secondary: 08A40: Operations, polynomials, primal algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 2 , October 1983 , pp. 194 - 196
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Pilz, G. (1977), Near-rings (North-Holland, Amsterdam-New York).Google Scholar
[2]Rao, V. Sambasiva, ‘A characterization of semi-prime ideals in near-rings’, J. Austral. Math. Soc. Ser. A 32 (1982), 212–214.CrossRefGoogle Scholar
[3]Van der Walt, A. P. J., ‘Prime ideals and nil radicals in near-rings’, Arch. Math. (Basel) 15 (1964), 408–414.CrossRefGoogle Scholar