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Keywords:
$0$-distributive poset; $0$-ideal; $\alpha $-ideal; prime ideal; semiprime ideal; dense ideal
$0$-distributive poset; $0$-ideal; $\alpha $-ideal; prime ideal; semiprime ideal; dense ideal
Summary:
The concept of a $0$-ideal in \mbox {$0$-distributive} posets is introduced. Several properties of $0$-ideals in $0$-distributive posets are established. Further, the interrelationships between $0$-ideals and \mbox {$\alpha $-ideals} in \mbox {$0$-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.
References:
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