Centralizers of BCI-algebras

[摘要] 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.

[学科分类] 数学（综合）

[关键词] BCI-algebras;centralizer;(pseudo) center;C-closed subalgebras;central (derived) ideal