$0$-ideals in $0$-distributive posets

@article{Mokbel2016,
abstract = {The concept of a $0$-ideal in $0$-distributive posets is introduced. Several properties of $0$-ideals in $0$-distributive posets are established. Further, the interrelationships between $0$-ideals and $\alpha $-ideals in $0$-distributive posets are investigated. Moreover, a characterization of prime ideals to be $0$-ideals in $0$-distributive posets is obtained in terms of non-dense ideals. It is shown that every $0$-ideal of a $0$-distributive meet semilattice is semiprime. Several counterexamples are discussed.},
author = {Mokbel, Khalid A.},
journal = {Mathematica Bohemica},
keywords = {$0$-distributive poset; $0$-ideal; $\alpha $-ideal; prime ideal; semiprime ideal; dense ideal},
language = {eng},
number = {4},
pages = {509-517},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$0$-ideals in $0$-distributive posets},
url = {http://eudml.org/doc/287570},
volume = {141},
year = {2016},
}

TY - JOUR
AU - Mokbel, Khalid A.
TI - $0$-ideals in $0$-distributive posets
JO - Mathematica Bohemica
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 141
IS - 4
SP - 509
EP - 517
AB - The concept of a $0$-ideal in $0$-distributive posets is introduced. Several properties of $0$-ideals in $0$-distributive posets are established. Further, the interrelationships between $0$-ideals and $\alpha $-ideals in $0$-distributive posets are investigated. Moreover, a characterization of prime ideals to be $0$-ideals in $0$-distributive posets is obtained in terms of non-dense ideals. It is shown that every $0$-ideal of a $0$-distributive meet semilattice is semiprime. Several counterexamples are discussed.
LA - eng
KW - $0$-distributive poset; $0$-ideal; $\alpha $-ideal; prime ideal; semiprime ideal; dense ideal
UR - http://eudml.org/doc/287570
ER -