International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3956 2020 2020 Department of Mathematics, College of Science, University of Anbar, Ramadi, Iraq Dunia Dunia AL-Mustansiriyah University, College of Science, Department of Mathematics, Baghdad, Iraq Amenah Hassan Ibrahim Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, Anbar, Iraq Majid Mohammed Abed The most important applications of an algebra like BCK-Algebra. As a generalization of ring, we study γ- semi-ring and γ-ring in invarianent neutrosophic set. Neutrosophic concepts are widely used in the field of mathematics and other sciences, especially in studying the Algebra. In this paper, we present the concept of neutrosophic γ-BCK-Algebras as an example of this generalization. We also present neutrosophic sub-algebra, neutrosophic ideal and some other type structure algebraic. We proved that if f : AI → N I is a homomorphism of neutrosophic γ-BCK-algebras AI and NI, then f is injective if and only if neutrosophic ker(f ) = {0I}. Also, we presented, if NI be a normal neutrosophic subalgebra of neutrosophic γ-BCK- algebra AI, then ” ∼ N I ” is a congruence relation. 2026 2026 10 18 10.54216/IJNS.270102 https://www.americaspg.com/articleinfo/21/show/3956