Some results on fuzzy prime spectrum of a ring

Abstract In this note we extend the results of Kumar (1992). In this context, we first give a counter-example to his Theorem 3.4(ii) and then we prove that the fuzzy prime spectrum of a ring and the elements of its basis are both compact. Finally, by giving two examples, we will show that it is not true in general, that any element of a basis of the fuzzy prime spectrum of a Boolean ring is closed, and the fuzzy prime spectrum itself is Hausdorff. Also by an example it is shown that the proof of the necessity of the condition of Theorem 5.3 of (Kumar, 1992) is incorrect.