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Keywords:
0-distributive lattice; $\alpha $-ideal; annihilator ideal; quasi-complemented lattice
0-distributive lattice; $\alpha $-ideal; annihilator ideal; quasi-complemented lattice
Summary:
In a 0-distributive lattice sufficient conditions for an $\alpha $-ideal to be an annihilator ideal and prime ideal to be an $\alpha $-ideal are given. Also it is proved that the images and the inverse images of $\alpha $-ideals are $\alpha $-ideals under annihilator preserving homomorphisms.
References:
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