Abstract

To interact three different types of prime bi-ideals are introduce and the relation between them is obtain. Also we have define three different mb -systems. The bi-ideal P of a ternary semiring R is 2-prime if and only if RML ⊆ P, where R is a right ideal, M is a lateral ideal and L is a left ideal of R, implies R ⊆ P or M ⊆ P or L ⊆ P. If B is a bi-ideal of R, then HB is the unique largest two-sided ideal of R contained B. Let M be a mb 3 system and bi-ideal B of R with B ∩ M = φ. Then there exists a 3-prime P of R containing B with P ∩ M = φ.