One can check that there exists a lattice which is finite. Let us mention that every lattice which is finite is also complete. Let L be a lattice and let D be a subset of the carrier of L . Let L be a finite lattice. Let L be a lattice.
L is co-noetherian.
One can verify that every lattice which is finite is also noetherian and every lattice which is finite is also co-noetherian. Let L be a lattice and let a , b be elements of the carrier of L . Let L be a lattice, a be an element of the carrier of L , and b , c be elements of the carrier of L such that b c . Let L be a noetherian lattice, a be an element of the carrier of L , and d be an element of the carrier of L . Suppose a d and a d .