On Neutrosophic of BE-Algebra

Marrwa A. Salih¹, Dunia A. Jarwan², Majid M. Abed^3,*

¹Department of Mathematics, College of Education for Pure Science, University of Tikrit, Tikrit, Iraq

²Department of Applied Mathematics, College of Science, University of Anbar, Anbar, Iraq

³Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, Anbar, Iraq

Emails: marrwaabdallah1984@tu.edu.iq; dunia.alawi@uoanbar.edu.iq; majid_math@uoanbar.edu.iq

Abstract

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  is called BE-algebra if   ∀ a ∈A, b, c ∈A  collect , 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).

Keywords: BE-algebra; Neutrosophic set; BE-filter; BE-subalgebra; Atom element