Self-dual lattice identities. (Q1771958)

Given a finitely based self-dual variety of lattices, there is the question whether it is definable by a single self-dual lattice identity. The authors use several methods producing a single identity which is equivalent to a finite set of given identities. Applying them, they show that there are infinitely many self-dual varieties of lattices with ``yes'' as the answer (e.g.\ modular, distributive, p-modular varieties) and infinitely many with the answer ``no''. Moreover, any self-dual lattice variety can be defined by a set of self-dual inequalities and, when finitely based, by a single self-dual inequality.