“School of Mathematics”
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| Paper IPM / M / 108 |
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| Abstract: | |||||
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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.
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