Mathematica Bohemica, Vol. 141, No. 4, pp. 509-517, 2016
$0$-ideals in $0$-distributive posets
Khalid A. Mokbel
Received March 27, 2014. First published October 13, 2016.
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.