Dual Skew Semi-Heyting Almost Distributive Lattices -by Berhanu Assaye, Mihret Alamneh and Yeshiwas Mebrat

# Dual Skew Semi-Heyting Almost Distributive Lattices-by Berhanu Assaye, Mihret Alamneh and Yeshiwas Mebrat

Abstract: In this paper we introduce the concept of dual skew SHADLs and characterize it in terms of dual SHADL. We define an equivalence relation $\theta$ on a dual skew SHADL $L$ and prove that $\theta$ is a congruence relation on the equivalence class $[x]\theta$ so that each congruence class is a maximal rectangular subalgebra and the quotient $[y]\theta/\theta$ is a maximal lattice image of $[x]\theta$ for any $y\in [x]\theta$. Also we show that if the set $PI(L)$ of all the principal ideals of an ADL $L$ with 0 is a dual skew semi-Heyting algebra then $L$ becomes a dual skew SHADL. Further we present different conditions on which an ADL with 0 becomes a dual skew SHADL.

Keywords:  dual semi-Heyting almost distributive lattice, dual semi-Heyting algebra and dual skew Heyting almost distributive lattice.