On elementary, odd, semimagic and other classes of antilattices

An antilattice is an algebraic structure based on the same set of axioms as a lattice except that two commutativity for ∧ and ∨ are replaced by anticommutative counterparts. In this paper, we study certain classes antilattices, including elementary (no nontrivial subantilattices), odd subantilattices order [Formula: see text]), simple congruences) irreducible (not expressible direct product). finite case, antilattices Leech’s Latin which arise from construction semimagic squares pairs orthogonal squares.