Closed and Dense Elements in Semi Heyting Almost Distributive Lattices


G. C. Rao, M. V. Ratnamani, Berhanu Assaye




In this paper, we define the concept of a closed element and dense element in a Semi Heyting Almost Distributive Lattice (SHADL) $L$ and derive some properties of closed elements and dense elements of $L$. We also observe that every SHADL is a pseudocomplemented ADL and that the set $L^*=\{x^*/x\in L\}$ of all closed elements of an SHADL $L$, forms a Boolean algebra with the operation $\veebar$ defined as $x\veebar y=(x^*\wedge y^*)^*$ for every $x,y\in L$ where, $x^*=(x\to0)\wedge m$.