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

Mathematica Bohemica (2016)

- Volume: 141, Issue: 4, page 509-517
- ISSN: 0862-7959

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topMokbel, Khalid A.. "$0$-ideals in $0$-distributive posets." Mathematica Bohemica 141.4 (2016): 509-517. <http://eudml.org/doc/287570>.

@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 -

## References

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