The summary purpose of this work: We extending certain results on α-centralizer of inverse semiring under specific conditions, achieve new results on lie ideal of inverse semiring with some consequent collieries, generalize assorted α-centralizer for lie ideal of inverse semiring with some collieries, investigate significant theorems on jordan α-centralizer of prime inverse semiring and we extend certain results of α-centralizers and jordan α-centralizers on lie-ideals of prime semi-rings to prime inverse semi-ring, we generalizing the results of Mary in to α-centralizer on semiring, Also we generalize our results on lie ideals of inverse semiring. We extending the results of Shafiq, Aslam, Javed to α- centralizer of Inverse semiring. since R is left (right) Jordan α-centralizer on”V, we get the output R is a left (right) α-centralizer on V.”If it where α is an automorphism of V,R(u) ∈ V, for any u ∈ V, and α(Z(V))= Z(V). We also get the following output R is a α-centralizer on V.
Centralizer on Lie-ideal of Semi-prime Inverse Semi-ring
Lie-ideal
prime inverse semi-ring
semi-prime inverse semi-ring
α-centralizer
jordan α-centralizer