Weakly 2-Absorbing Ideals in Almost Distributive Lattices

Abstract

The concepts of weakly 2-absorbing ideal and weakly 1-absorbing prime ideal in an almost distributive lattice (ADL) are introduced, and the necessary conditions for a weakly 1-absorbing prime ideal to become a weakly 2-absorbing ideal in algebraic form are proved. Also, weakly 2-absorbing ideals are characterized in terms of weakly prime ideals and 2-absorbing ideals. Finally, the lattice epimorphic images and inverse images of the weakly 2-absorbing ideal and weakly 1-absorbing prime ideal are discussed.