A module theoretic characterization of the prime radical of near-rings. (English) Zbl 1441.16051
Summary: A prime right \(R\)-group is introduced for a right near-ring \(R\). A characterization of a prime ideal of a near-ring \(R\) is given in terms of the annihilator of a prime right \(R\)-group of the near-ring \(R\). Using it a module theoretic characterization of the prime radical of near-rings is presented. Also it is re-established that the prime radical of near-rings is a Hoehnke radical (H-radical) which is idempotent but not complete using this module theoretic characterization of the prime radical of near-rings.
Keywords:
near-ring; right \(R\)-group; prime right \(R\)-group; prime radical; Kurosh-Amitsur radicalReferences:
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