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.
@article{bwmeta1.element.doi-10_1515_math-2016-0047,
author = {Ninghua Gao and Qingguo Li and Zhaowen Li},
title = {When doL-fuzzy ideals of a ring generate a distributive lattice?},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {531-542},
zbl = {1347.06016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0047}
}
Ninghua Gao; Qingguo Li; Zhaowen Li. When doL-fuzzy ideals of a ring generate a distributive lattice?. Open Mathematics, Tome 14 (2016) pp. 531-542. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0047/