When doL-fuzzy ideals of a ring generate a distributive lattice?

• Autorzy: Ninghua Gao , Qingguo Li , Zhaowen Li
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Boolean ring; Complete Heyting algebra; L-fuzzy extended ideals; L-fuzzy ideals

Kategorie tematyczne

• 06B05: Structure theory
• 28A60: Measures on Boolean rings, measure algebras

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 531-542

Daty

wydano

2016-01-01

otrzymano

2016-04-07

zaakceptowano

2016-06-28

online

2016-07-23

Twórcy

autor

Ninghua Gao

• College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, 410082

autor

Qingguo Li

• College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, 410082

autor

Zhaowen Li

• College of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, Guangxi, 530006

Identyfikatory

DOI

10.1515/math-2016-0047