  A mixed lattice is a lattice-type structure consisting of a set with two
partial orderings, and generalizing the notion of a lattice. Mixed lattice
theory has previously been studied in various algebraic structures, such as
groups and semigroups, while the more general notion of a mixed lattice remains
unexplored. In this paper, we study the fundamental properties of mixed
lattices and the relationships between the various properties, such as the
one-sided associative, distributive and modular laws. We also give an
alternative definition of mixed lattices and mixed lattice groups as
non-commutative and non-associative algebras satisfying a certain set of
postulates. The algebraic and the order-theoretic definitions are then shown to
be equivalent.
