Some results on commutative BI-Algebras‎

Abstract

‎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.

Keywords

• bi-algebra‎
• ‎(branchwise) commutative‎
• ‎distributive‎
• ‎(commutative) ideal