ON Q-ALGEBRAS

We introduce a new notion, called a Q-algebra, which is a generalization of the idea of BCH /BCI /BCK -algebras and we generalize some theorems discussed in BCI -algebras. Moreover, we introduce the notion of “quadratic” Q-algebra, and show that every quadratic Q-algebra (X; ∗, e), e ∈ X, has a product of the form x ∗ y = x − y + e, where x, y ∈ X when X is a field with |X| ≥ 3.

2000 Mathematics Subject Classification. 06F35, 03G25.