Abstract
In this paper, we discuss normal subalgebras in BI-algebras and obtain the quotient BI-algebra which is useful for the study of structures of BI-algebras. Moreover, we obtain several conditions for obtaining BI-algebras on the non-negative real numbers by using an analytic methods.
Highlights
Borumand Saeid et al ([1]) introduced a new algebra, called a BI-algebra, which is a generalization of both a implication algebra and an implicative BCK-algebra, and they discussed the basic properties of BI-algebras, and investigated some ideals and congruence relations
We discuss normal subalgebras in BI-algebras and obtain the quotient BI-algebra which is useful for the study of structures of BI-algebras
We introduce a relation “≤” on a BI-algebra X by x ≤ y if and only if x ∗ y = 0
Summary
S. Kim ([7]) introduced the notion of d-algebras, which is another useful generalization of BCKalgebras, and investigated several relations between d-algebras and BCK-algebras, and investigated other relations between d-algebras and oriented digraphs. A. Borumand Saeid et al ([1]) introduced a new algebra, called a BI-algebra, which is a generalization of both a (dual) implication algebra and an implicative BCK-algebra, and they discussed the basic properties of BI-algebras, and investigated some ideals and congruence relations. S. Kim ([7]) gave an analytic method for constructing proper examples of a great variety of non-associative algebra of the BCK-type and generalizations of these. Kim ([7]) gave an analytic method for constructing proper examples of a great variety of non-associative algebra of the BCK-type and generalizations of these They made several useful (counter-)examples using analytic method.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
