A rotational lattice is a structure where is a lattice and is a lattice automorphism of finite order. We describe the subdirectly irreducible distributive rotational lattices. Using Jónsson’s lemma, this leads to a description of all varieties of distributive rotational lattices.
In this paper the notion of weak chain-completeness is introduced for pseudo-ordered sets as an extension of the notion of chain-completeness of posets (see [3]) and it is shown that every isotone map of a weakly chain-complete pseudo-ordered set into itself has a least fixed point.
Let be a finite lattice with a least element 0. is an annihilating-ideal graph of in which the vertex set is the set of all nontrivial ideals of , and two distinct vertices and are adjacent if and only if . We completely characterize all finite lattices whose line graph associated to an annihilating-ideal graph, denoted by , is a planar or projective graph.