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

Ninghua Gao; Qingguo Li; Zhaowen Li

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 531-542
- ISSN: 2391-5455

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topNinghua 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 -

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