O-ideals in Almost Distributive Lattices
CJM Vol. 3 (December 2011), pp. 13 – 24.
Abstract:
Concept of O-ideals is introduced in an Almost Distributive Lattice and these O-ideals are characterized in terms of minimal prime ideals. A necessary and sufficient condition for the zero ideal of an ADL to become an O-ideal is derived. $\star$-ADLs are characterized in terms of their O-ideals and $α$-ideals. Finally, a set of equivalent conditions are established for every O-ideal of an ADL to become a principal ideal.
2000 Mathematics Subject Classification:
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