MMN-2632

# Centralizers of BCI-algebras

**A. Najafi**, Department of Mathematics, Behbahan Branch, Islamic Azad University, Behbahan, Iran,`najafi@behiau.ac.ir`

**A. Borumand Saeid**, Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Pajoohesh Sq., Imam Khomeni Highway, 7616913439 Kerman, Iran,`arsham@uk.ac.ir`

**E. Eslami**, Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Pajoohesh Sq., Imam Khomeni Highway, 7616913439 Kerman, Iran,`eslami@uk.ac.ir`

## Abstract

In this paper, the concept of the centralizer of a subset (an element) of a BCI-algebra by using commutators is given. The connection between commutative ideals with commutators are considered. Also the pseudo center of a BCI-algebra is defined and the relationships between center and pseudo center in BCI-algebras are
discussed. Following the concept of the centralizer, we introduce C-closed subalgebras of a BCI-algebra and discuss some characteristics of these subalgebras. Finally, we define central ideal and derived ideal of a BCI-algebra and the relationship between central ideal, derived ideal
and other ideals of BCI-algebras are investigated.

Vol. 22 (2021), No. 1, pp. 407-425

DOI: 10.18514/MMN.2021.2632