Abstract
Basic properties of branches of pseudo-BCH algebras are described. Next, the concept of a branchwise commutative pseudo-BCH algebra is introduced. Some conditions equivalent to branchwise commutativity are given. It is proved that every branchwise commutative pseudo-BCH algebra is a pseudo-BCI algebra.
Highlights
In 1966, Imai and Iseki ([9, 13]) introduced BCK and BCI algebras
It is known that BCK and BCI algebras are contained in the class of BCH algebras
We show that every such algebra is a pseudo-BCI algebra
Summary
In 1966, Imai and Iseki ([9, 13]) introduced BCK and BCI algebras. In 1983, Hu and Li ([8]) defined BCH algebras. A pseudo-BCH algebra X is said to be commutative if for all x, y ∈ X, it satisfies the following identities: (3) Following [4], we say that a pseudo-BCH algebra X is branchwise commutative if identities (3) and (4) hold for x and y belonging to the same branch.
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