Abstract
AbstractWe 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.
Publisher
Springer Science and Business Media LLC
Reference17 articles.
1. D Adnadjevic. Dimension of fuzzy ordered sets, Fuzzy Sets and Systems, 1994, 67: 349–357.
2. D D Anderson, D E Dobbs, M Zafrullah. Some applications of Zorn’s lemma in algebra, Tamkang Journal of mathenatics, 2009, 40(2): 139–150.
3. I Beg. On fuzzy Zorn’s lemma, Fuzzy Sets and Systems, 1999, 101: 181–183.
4. G M Bergman. An invitation to general algebra and universal constructions, Henry Helson, Berkeley, CA, 1998.
5. E W Chapin Jr. Set valued set theory, Parts I and II, Notre Dame J Formal Logic, 1974, XV(4): 619–634, 1975, XVI(2): 255–267.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献