-ideals in -distributive posets
The concept of a -ideal in -distributive posets is introduced. Several properties of -ideals in -distributive posets are established. Further, the interrelationships between -ideals and -ideals in -distributive posets are investigated. Moreover, a characterization of prime ideals to be -ideals in -distributive posets is obtained in terms of non-dense ideals. It is shown that every -ideal of a -distributive meet semilattice is semiprime. Several counterexamples are discussed.