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

Ninghua Gao, Qingguo Li, and Zhaowen Li. "When doL-fuzzy ideals of a ring generate a distributive lattice?." Open Mathematics 14.1 (2016): 531-542. <http://eudml.org/doc/285430>.

@article{NinghuaGao2016,
abstract = {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.},
author = {Ninghua Gao, Qingguo Li, Zhaowen Li},
journal = {Open Mathematics},
keywords = {Boolean ring; Complete Heyting algebra; L-fuzzy extended ideals; L-fuzzy ideals; complete Heyting algebra; -fuzzy extended ideals; -fuzzy ideals},
language = {eng},
number = {1},
pages = {531-542},
title = {When doL-fuzzy ideals of a ring generate a distributive lattice?},
url = {http://eudml.org/doc/285430},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Ninghua Gao
AU - Qingguo Li
AU - Zhaowen Li
TI - When doL-fuzzy ideals of a ring generate a distributive lattice?
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 531
EP - 542
AB - 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.
LA - eng
KW - Boolean ring; Complete Heyting algebra; L-fuzzy extended ideals; L-fuzzy ideals; complete Heyting algebra; -fuzzy extended ideals; -fuzzy ideals
UR - http://eudml.org/doc/285430
ER -