Some Basic Properties of Completely Prime Ideals in Near Rings
DOI:
https://doi.org/10.5614/j.math.fund.sci.2015.47.3.1Keywords:
completely prime ideal, near-ring, quasi completely prime, weakly completely prime ideal, weakly quasi completely primeAbstract
In this investigation we studied completely prime, weakly completely prime, quasi completely prime and weakly quasi completely prime ideals in near-rings. Some characterizations of completely prime and weakly completely prime ideals were obtained. Moreover, we investigated relationships between completely prime and weakly completely prime ideals in near-rings. Finally, we obtained necessary and sufficient conditions for a weakly completely prime ideal to be a completely prime ideal.References
Pilz, G. Near-Rings: The Theory and Its Applications, Mathematic Studies, 23, North-Holland Publishing Company, Amsterdam, 1977.
Holcombe, W.M.L., Primitive Near-Rings, Doctoral Dissertation, University of Leeds, 1970.
Groenewald, N.J., The Completely Prime Radical in Near-Rings, Acta Math. Hung., 33, pp. 301-305, 1988.
Groenewald, N.J., Different Prime Ideals in Near-Rings, Comm. Algebra, 19(10), pp. 2667-2675, 1991.
Anderson, D.D. & Smith, E., Weakly Prime Ideals, Houston J. Math., 29(4), pp. 831-840, 2003.
Abbass, H.H. & Mohammed, M.A., On Completely Prime Ideal with Respect to an Element of a Near Ring. Journal of Kerbala University, 10(3), pp. 285-301, 2012.
Meldrum, J.D.P., Near-Rings and their Links with Groups, Research notes in Math. Pitman, London, 134, 1985.
