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P-STRONGLY REGULAR NEAR-RINGS

  • Dheena, P. (Department of Mathematics Annamalai University) ;
  • Jenila, C. (Department of Mathematics Annamalai University)
  • Received : 2011.04.27
  • Published : 2012.07.31

Abstract

In this paper we introduce the notion of P-strongly regular near-ring. We have shown that a zero-symmetric near-ring N is P-strongly regular if and only if N is P-regular and P is a completely semiprime ideal. We have also shown that in a P-strongly regular near-ring N, the following holds: (i) $Na$ + P is an ideal of N for any $a{\in}N$. (ii) Every P-prime ideal of N containing P is maximal. (iii) Every ideal I of N fulfills I + P = $I^2$ + P.

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