$\alpha$-ideals in $0$-distributive posets

Mokbel, Khalid A.. "$\alpha $-ideals in $0$-distributive posets." Mathematica Bohemica 140.3 (2015): 319-328. <http://eudml.org/doc/271604>.

@article{Mokbel2015,
abstract = {The concept of $\alpha $-ideals in posets is introduced. Several properties of $\alpha $-ideals in $0$-distributive posets are studied. Characterization of prime ideals to be $\alpha $-ideals in $0$-distributive posets is obtained in terms of minimality of ideals. Further, it is proved that if a prime ideal $I$ of a $0$-distributive poset is non-dense, then $I$ is an $\alpha $-ideal. Moreover, it is shown that the set of all $\alpha $-ideals $\alpha \mathop \{\rm Id\}(P)$ of a poset $P$ with $0$ forms a complete lattice. A result analogous to separation theorem for finite $0$-distributive posets is obtained with respect to prime $\alpha $-ideals. Some counterexamples are also given.},
author = {Mokbel, Khalid A.},
journal = {Mathematica Bohemica},
keywords = {$0$-distributive poset; ideal; $\alpha $-ideal; prime ideal; non-dense ideal; minimal ideal; annihilator ideal},
language = {eng},
number = {3},
pages = {319-328},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$\alpha $-ideals in $0$-distributive posets},
url = {http://eudml.org/doc/271604},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Mokbel, Khalid A.
TI - $\alpha $-ideals in $0$-distributive posets
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 3
SP - 319
EP - 328
AB - The concept of $\alpha $-ideals in posets is introduced. Several properties of $\alpha $-ideals in $0$-distributive posets are studied. Characterization of prime ideals to be $\alpha $-ideals in $0$-distributive posets is obtained in terms of minimality of ideals. Further, it is proved that if a prime ideal $I$ of a $0$-distributive poset is non-dense, then $I$ is an $\alpha $-ideal. Moreover, it is shown that the set of all $\alpha $-ideals $\alpha \mathop {\rm Id}(P)$ of a poset $P$ with $0$ forms a complete lattice. A result analogous to separation theorem for finite $0$-distributive posets is obtained with respect to prime $\alpha $-ideals. Some counterexamples are also given.
LA - eng
KW - $0$-distributive poset; ideal; $\alpha $-ideal; prime ideal; non-dense ideal; minimal ideal; annihilator ideal
UR - http://eudml.org/doc/271604
ER -