International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3175 2020 2020 Department of Mathematics, College of Education for Pure Science, University of Tikrit, Tikrit, Iraq Majid Majid Department of Applied Mathematics, College of Science, University of Anbar, Anbar, Iraq Dunia A. Jarwan Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, Anbar, Iraq Majid M. Abed The BE-Algebra was presented by Kim in 2007. After that, several authors studied this type of logic concept in algebra. In this paper, we introduce more properties and remarks of BE-Algebra. Note that (A,*,1) is called BE-algebra if   ∀ a ∈A, b, c ∈A: collect a*a=1, a*1=1, 1*a=a and a*(b*c)=b*(a*c). In addition, a Neutrosophic BE-filter FI subset of the Neutrosophic BE-algebra is Neutrosophic BE-algebra AI is Neutrosophic BE-subalgebra AI.  Some new results and the criterion to determine some properties of BE-algebra and several relationships with another algebra namely Hibert algebras (H-algebra). 2025 2025 206 211 10.54216/IJNS.250218 https://www.americaspg.com/articleinfo/21/show/3175