Commutators in BCI-algebras

Article type: Research Article

Authors: Najafi, Ardavan^a | Borumand Saeid, Arsham^{b; *} | Eslami, Esfandiar^b

Affiliations: [a] Department of Mathematic, Islamic Azad University, Behbahan Branch, Behbahan, Iran | [b] Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

Correspondence: [*] Corresponding author. Arsham Borumand Saeid, Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran. Tel.: +98 34 31322490; E-mail: [email protected].

Abstract: In this paper, the notions of commutators and pseudo commutators of elements (subsets) of a BCI-algebra are introduced and some properties are given. The concept of solvable BCI-algebras are also discussed and their properties are investigated. It is proved that the class of solvable BCI-algebras is closed under sub-algebra, cartesian product and inverse image operations.

Keywords: BCI-algebras, (pseudo) commutators, derived sub-algebra, solvable BCI-algebras

DOI: 10.3233/IFS-162148

Journal: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 1, pp. 357-366, 2016