Theory of PO-?-Ideals and PO-?-Filters in PO-?-Semigroups

The concept of a semigroup is very simple and plays a large role in the development of Mathematics. The theory of semigroups is similar to group theory and ring theory. The earliest major contributions to the theory of semigroups are strongly motivated by comparisons with groups and rings. Semigroup theory can be considered as one of the most successful off-springs of ring theory in the sense that the ring theory gives a clue how to develop the ideal theory of semigroups.