대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제27권3호
  • /
  • Pages.483-488
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  • 2012
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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P-STRONGLY REGULAR NEAR-RINGS

  • Dheena, P. (Department of Mathematics Annamalai University) ;
  • Jenila, C. (Department of Mathematics Annamalai University)
  • 투고 : 2011.04.27
  • 발행 : 2012.07.31
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초록

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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참고문헌

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  3. S. J. Choi, Quasiideals of a P-Regular Near-Ring, Int. J. Algebra 4 (2010), no. 9-12, 501-506.
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  6. G. Pilz, Near-Rings, North-Holland, Amsterdam, 1983.
  7. I. Yakabe, Regular near-rings without nonzero nilpotent elements, Proc. Japan Acad. Ser. A Math. Sci. 65 (1989), no. 6, 176-179. https://doi.org/10.3792/pjaa.65.176