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...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.展开更多
基金Supported by the National Natural Science Foundation of China(11971384)by the grant of Natural Science Basic Research Program of Shaanxi(Program No.2021JM-137)the Fundamental Research Funds for the Central Universities under grant QTZX2106,China 111 Project(B16037)and OPPO Research Fund.
文摘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.
