LA - SEMIRINGS In Which (S,.) Is Anti-Inverse Semigroup

This paper deals with the some results on LA– Semirings in which(s, ▪) is anti-inverse semigroup. In the first case of the LA - Semiring (S, +, .) satisfying the identity a+1 = 1, for all a in S then it is proved that (S, +) is anti-inverse semigroup. It is also proved that if (S, +,▪) is a LA – Semiring satisfying the above identity then (S, +) is an abelian semigroup and sum of two anti inverse elements is again anti inverse element in (S, +) and also proved that (S, +, ▪) is medial semiring. In this second case we consider LA- semiring (S, +, ▪) in which (s, ▪) is anti-inverse semigroup satisfying the identity a+1= a for all a in S then (S, +) is anti inverse semigroup and sum of two inverse elements is again anti inverse element in (S, +). It is also proved that in LA semiring in which (s, ▪) is anti-inverse semigroup then (S, +) is an abelian semigroup and the product of two inverse elements is again inverse element in (s, ▪).