  Skew lattices are non-commutative generalizations of lattices, and the cosets
represent the building blocks that skew lattices are built of. As by Leech's
Second Decomposition Theorem any skew lattice embeds into a direct product of a
left-handed skew lattice by a right-handed one, it is natural to consider the
so called flat coset decompositions, i.e. decompositions of a skew lattice into
right and left cosets, thus finding the smallest atoms that compose the
structure.
