Fuzzy Zorn’s lemma with applications  

作　　者：XIN Xiao-long FU Yu-long 

机构地区：[1]School of Science,Xi’an Polytechnic University,Xi’an 710048,China [2]School of Mathematics,Northwest University,Xi’an 710127,China [3]School of Cyber Engineering,Xidian University,Xi’an 710071,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2021年第4期521-536,共16页高校应用数学学报（英文版）（B辑）

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.

摘　　要：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.

关 键 词：fuzzy axioms of choice fuzzy Zorn’s lemma fuzzy well-ordering principle fuzzy ideal of a ring fuzzy Tychonoff Theorem 

分 类 号：O159[理学—数学]