Geodesic
On ideals in De Morgan residuated lattices
Kybernetika, Tome 54 (2018) no. 3, pp. 443-475.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In this paper, we introduce a new class of residuated lattices called De Morgan residuated lattices, we show that the variety of De Morgan residuated lattices includes important subvarieties of residuated lattices such as Boolean algebras, MV-algebras, BL-algebras, Stonean residuated lattices, MTL-algebras and involution residuated lattices. We investigate specific properties of ideals in De Morgan residuated lattices, we state the prime ideal theorem and the pseudo-complementedness of the ideal lattice, we pay attention to prime, maximal, $\odot$-prime ideals and to ideals that are meet-irreducible or meet-prime in the lattice of all ideals. We introduce the concept of an annihilator of a given subset of a De Morgan residuated lattice and we prove that annihilators are a particular kind of ideals. Also, regular annihilator and relative annihilator ideals are considered.
DOI : 10.14736/kyb-2018-3-0443
Classification : 03B22, 03G05, 03G25, 06A06, 08A72
Keywords: residuated lattice; De Morgan laws; filter; deductive system; ideal; $\cap $-prime; $\cap $-irreducible; annihilator 
@article{10_14736_kyb_2018_3_0443,
     author = {Holdon, Liviu-Constantin},
     title = {On ideals in {De} {Morgan} residuated lattices},
     journal = {Kybernetika},
     pages = {443--475},
     publisher = {mathdoc},
     volume = {54},
     number = {3},
     year = {2018},
     doi = {10.14736/kyb-2018-3-0443},
     mrnumber = {3844827},
     zbl = {06987017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-3-0443/}
}
TY  - JOUR
AU  - Holdon, Liviu-Constantin
TI  - On ideals in De Morgan residuated lattices
JO  - Kybernetika
PY  - 2018
SP  - 443
EP  - 475
VL  - 54
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-3-0443/
DO  - 10.14736/kyb-2018-3-0443
LA  - en
ID  - 10_14736_kyb_2018_3_0443
ER  - 
%0 Journal Article
%A Holdon, Liviu-Constantin
%T On ideals in De Morgan residuated lattices
%J Kybernetika
%D 2018
%P 443-475
%V 54
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-3-0443/
%R 10.14736/kyb-2018-3-0443
%G en
%F 10_14736_kyb_2018_3_0443
Holdon, Liviu-Constantin. On ideals in De Morgan residuated lattices. Kybernetika, Tome 54 (2018) no. 3, pp. 443-475. doi : 10.14736/kyb-2018-3-0443. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-3-0443/

Cité par Sources :