【摘 要】
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We introduced the fuzzy axioms of choice,fuzzy Zorn\'s lemma and fuzzy well-ordering principle,which are the fuzzy versions of the axioms of choice,Zorn\'s lemma and well-ordering principle,and discussed the relations among them.As an application of f
【机 构】
：
School of Science,Xi’an Polytechnic University,Xi’an 710048,China;School of Mathematics,Northwest Un
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We introduced the fuzzy axioms of choice,fuzzy Zorn\'s lemma and fuzzy well-ordering principle,which are the fuzzy versions of the axioms of choice,Zorn\'s lemma and well-ordering principle,and discussed the relations among them.As an application of fuzzy Zorn\'s lemma,we got the following results:(1) Every proper fuzzy ideal of a ring was contained in a maximal fuzzy ideal.(2) Every nonzero ring contained a fuzzy maximal ideal.(3) Introduced the notion of fuzzy nilpotent elements in a ring R,and proved that the intersection of all fuzzy prime ideals in a commutative ring R is the union of all fuzzy nilpotent elements in R.(4)Proposed the fuzzy version of Tychonoff Theorem and by use of fuzzy Zorn\'s lemma,we proved the fuzzy Tychonoff Theorem.
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