Generalized α-stone Almost Distributive Lattices and Prime α-ideals

摘要

The concept of prime a-ideals is introduced in an Almost Distributive Lattice (ADL) R. The existence of a prime α-idcal in an ADL is proved. A necessary and sufficient condition for a non-dense α-ideal to become a prime ideal is derived. The concept of a generalized α-Stone ADL is introduced and these classes of ADLs are characterized in terms of their prime α-ideals. Finally, an equivalency is obtained between a ★-ADL and a generalized α-Stone ADL.