Some Study of Semigroups of -Bi-Ideals of Semirings.

Semigroups are generalizations of groups and rings. In the semigroup theory, there are certain kinds of band decompositions which are useful in the study of the structure of semigroups. This research will open up new horizons in the field of mathematics by aiming to use semigroup of -bi-ideal of semiring with semilattice additive reduct. With the course of this research, it will prove that subsemigroup, the set of all right -bi-ideals, and set of all left -bi-ideals are bands for -regular semiring. Moreover, it will be demonstrated that if semigroup of all -bi-ideals ((), ∗) is semilattice, then is -Clifford. This research will also explore the classification of minimal -bi-ideal.