When do L-fuzzy ideals of a ring generate a distributive lattice?

• Main Authors: Gao Ninghua, Li Qingguo, Li Zhaowen
• Format: Article
• Language: English
• Published: De Gruyter 2016-01-01
• Series: Open Mathematics
• Subjects: boolean ring; complete heyting algebra; l-fuzzy extended ideals; l-fuzzy ideals; 28a60; 06b05
• Online Access: https://doi.org/10.1515/math-2016-0047

The notion of L-fuzzy extended ideals is introduced in a Boolean ring, and their essential properties are investigated. We also build the relation between an L-fuzzy ideal and the class of its L-fuzzy extended ideals. By defining an operator “⇝” between two arbitrary L-fuzzy ideals in terms of L-fuzzy extended ideals, the result that “the family of all L-fuzzy ideals in a Boolean ring is a complete Heyting algebra” is immediately obtained. Furthermore, the lattice structures of L-fuzzy extended ideals of an L-fuzzy ideal, L-fuzzy extended ideals relative to an L-fuzzy subset, L-fuzzy stable ideals relative to an L-fuzzy subset and their connections are studied in this paper.