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Completely Prime Ideals and Radicals in Near-Rings

Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 336)

Abstract

An ideal I of a near-ring R is 2-primal if the prime radical of R/I equals the set of nilpotent elements of R/I We show that if \(IR\subseteq I\), then I is a 2-primal ideal of R if and only if each minimal prime ideal containing I is a completely prime ideal. A complete classification of the subdirectly irreducible zero symmetric near-rings with a 2-primal heart is provided. Zero symmetric near-rings with each prime ideal completely prime are classified in terms of the 2-primal condition. Various chain conditions are invoked on 2-primal near-rings to obtain decompositions and additive group information.

Keywords

Prime Ideal Prime Radical Homomorphic Image Nilpotent Element Matrix Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Southwestern LouisianaLafayetteUSA

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