Akefe Radfar - Department of Mathematics, Payame Noor University, p.o.box. ۱۹۳۹۵-۳۶۹۷, Tehran, Iran
Shahriar Soleymani - Department of Mathematics, Payame Noor University, p.o.box. ۱۹۳۹۵-۳۶۹۷, Tehran, Iran
Akbar Rezaei - Department of Mathematics, Payame Noor University, p.o.box. ۱۹۳۹۵-۳۶۹۷, Tehran, Iran

‎The notion of a (branchwise) commutative BI-algebra is presented, and some related properties are investigated. We show that the class of commutative BH-algebras is broader than the class of commutative BI-algebras. Moreover, we %show that prove every  singular BI-algebra is a BH-algebra. Also, we define the  commutative ideals in BI-algebras and characterize the commutative BI-algebras in terms of commutative ideals.

BI-algebra‎, ‎(Branchwise) Commutative‎, ‎Distributive‎, ‎(Commutative) Ideal