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


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