Abstract
Abstract We define ab initio the fuzzy nil radical of an ideal of a commutative ring R . The definition has been successful in establishing the analogues of most of the fundamental ground results involving radicals in the fuzzy setting. The concept of a fuzzy semiprime ideal of a commutative ring R is introduced through the fuzzy nil radical of an ideal. A commutative regular ring is characterized by its semiprime ideals. At the end we demonstrate that the intersection of all fuzzy semiprime ideals of a commutative ring which contain a given fuzzy ideal λ is precisely the nil radical √λ of λ. This establishes the vital connection between a fuzzy semiprime ideal and the nil radical of a fuzzy ideal.
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