Neutrosophic of γ-BCK -Algebra
Dunia Alawi Jarwan1,∗, Amenah Hassan Ibrahim2, Majid Mohammed Abed3
1Department of Mathematics, College of Science, University of Anbar, Ramadi, Iraq
2AL-Mustansiriyah University, College of Science, Department of Mathematics, Baghdad, Iraq
3Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, Anbar,
Iraq
Emails: dunia.alawi@uoanbar.edu.iq; amena 1335723@uomustansiriyah.edu.iq;
majid math@uoanbar.edu.iq
Abstract
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.
Kewords: BCK -Algebra; Semi-ring; Neutrosophic logic; Neutrosophic Set; Simple submodule