Completely Regular Semiring

Semiring theory is one of the most developing branch of Mathematics with wide application in many disciplines such as Computer Science. Coding theory, Topology space and many researchers studies different structure of semirings like complemented semirings, Boolean like semirings etc. In this paper, we discuss some properties of Completely regular semiring, In this paper, we have many proved criteria on the different structure of semirings, Anti-inverse (S, +) and quasi-separative (S,. ) is proved through completely regular semiring application, completely regular semiring a + x = a is proved, as Distributive, (S, +) is a Boolean ring. On the condition of completely regular semiring anti-inverse is proved as monosemiring and some other relations are proved. We determine the additive and multiplicative structures of a Completely regular semiring by assuming different properties on the additive (multiplicative) structures. x