- FUZZY IDEALS IN NEAR-RINGS
- Hong, Sung-Min ; Jun, Young-Bae ; Kim, Hee-Sik ;
- Bulletin of the Korean Mathematical Society, volume 35, issue 3, 1998, Pages 455~464
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.