Data de publicação: Jan 22, 2013 12:53:30 PM
Just before the closing of 2012, the paper "On ideals of a skew lattice" under arXiv with the reference arXiv:1207.0231, has been released in DM. Discussiones Mathematicae - General Algebra and Applications. This journal is devoted to Classical and General Algebra with its applications to Computer Science and Combinatorics, and publishes high-quality refereed original papers and may also include research problems.
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. This paper focus on the study of ideals in the context of skew lattices where 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.