Annulets in almost distributive lattice

Abstract

We introduce the concept of annulets in an Almost Distributive lattice(ADL) R with 0. We characterize both generalized stone ADL and normal ADL in terms of their annulets. We characterize ⋆-ADLs by means of their annulets. It is proved that the lattice A0(R) of all annulets of a generalized stone ADL R is a relatively complemented sublattice of the lattice I (R) of all ideals of R. Finally, it is proved that A0(R) is relatively complemented iff R is sectionally ⋆-ADL.