Ideals are one of the main topics of interest to the study of the order
structure of an algebra. Due to their nice properties, ideals have an important
role both in lattice theory and semigroup theory. Two natural concepts of ideal
can be derived, respectively, from the two concepts of order that arise in the
context of skew lattices. The correspondence between the ideals of a skew
lattice, derived from the preorder, and the ideals of its respective lattice
image is clear. Though, skew ideals, derived from the partial order, seem to be
closer to the specific nature of skew lattices. In this paper we review ideals
in skew lattices and discuss the intersection of this with the study of the
coset structure of a skew lattice.Comment: 16 page
