  A mixed lattice vector space is a partially ordered vector space with two
partial orderings and certain lattice-type properties. In this paper we first
give some fundamental results in mixed lattice groups, and then we investigate
the structure theory of mixed lattice vector spaces, which can be viewed as a
generalization of the theory of Riesz spaces. More specifically, we study the
properties of ideals and bands in mixed lattice spaces, and the related idea of
representing a mixed lattice space as a direct sum of disjoint bands. Under
certain conditions, these decompositions can also be given in terms of order
projections.
