Dual skew Heyting almost distributive lattices

Abstract

In this paper, we introduce the concept of dual skew Heyting almost distributive lattices (dual skew HADLs) and characterise it in terms of dual HADL. We define an equivalence relation θ on a dual skew HADL L and prove that θ is a congruence relation on the equivalence class [x]θ so that each congruence class is a maximal rectangular subalgebra and the quotient [y]θ/θ is a maximal lattice image of [x]θ for any y ∈ [x]θ. Moreover, we show that if the set PI (L) of all the principal ideals of an ADL L with 0 is a dual skew Heyting algebra then L becomes a dual skew HADL. Further we present different conditions on which an ADL with 0 becomes a dual skew HADL.

Keywords

• almost distributive lattice (adl)
• maximal element
• heyting almost distributive lattice(hadl)
• heyting algebra
• skew lattice
• skew heyting algebra and skew heyting almost distributive lattice(skew hadl)
• 03g12
• 06d15