On elementary, odd, semimagic and other classes of antilattices

Abstract

An \emph{antilattice} is an algebraic structure based on the same set of axioms as a lattice except that the two commutativity axioms for $\wedge$ and $\vee$ are replaced by anticommutative counterparts. In this paper we study certain classes of antilattices, including elementary (no nontrivial subantilattices), odd (no subantilattices of order $2$), simple (no nontrivial congruences) and irreducible (not expressible as a direct product). In the finite case, odd antilattices are the same as Leech's \emph{Latin} antilattices which arise from the construction of semimagic squares from pairs of orthogonal Latin squares.

24 pages, 3 figures

References in corpus (1)

• Regular Antilattices