$\sigma$-Prime Spectrum of Almost Distributive Lattices

Abstract

For each $\alpha$-ideal of an almost distributive lattice (ADL) to become a $\sigma$-ideal, a set of equivalent conditions is derived, which tends to result in a characterization of generalized Stone ADLs. On an ADL, a one-to-one correspondence is derived between the set of all prime $\sigma$-ideals of the ADL and the set of all prime $\sigma$-ideals of the quotient ADL. Finally, proved some properties of prime $\sigma$-ideals of a normal ADL topologically.