Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/2403 2022 2022 Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq Sundus taha kathem Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq Abdulrahman Hameed Majeed The concept of inverse Γ-semiring   M is a generalization of inverse semiring. This paper investigates the concept (σ, τ)- derivation on inverse Γ-semiring and extend a few results of this map on prime inverse Γ- semiring that acts as a homomorphism or as an anti- homomorphism, where σ, τ are automorphisms on M. 2023 2023 39 55 10.54216/GJMSA.0100105 https://www.americaspg.com/articleinfo/33/show/2403