Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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FUZZY IDEALS IN NEAR-RINGS

  • Hong, Sung-Min (DEPARTMENT OF MATHEMATICS, GYEONG-SANG NATIONAL UNIVERSITY) ;
  • Jun, Young-Bae (DEPARTMENT OF MATHEMATICS, GYEONG-SANG NATIONAL UNIVERSITY) ;
  • Kim, Hee-Sik (DEPARTMENT OF MATHEMATICS, HANYANG UNIVERSITY)
  • Published : 1998.08.01
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Abstract

In this paper, we give another proof of Theorem 2.13 of [4] without using the sup property. For the homomorphic image $f(\mu)$ and preimage $f^{-1}(\nu)$ of fuzzy left (resp. right) ideals $\mu$ and $\nu$ respectively, we establish the chains of level left (resp. right) ideals of $f(\mu)$ and $f^{-1}(\nu)$, respectively. Moreover, we prove that a necessary condition for a fuzzy ideal $\mu$ of a near-ring $R$ to be prime is that $\mu$ is two-valued.

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