摘要
设(X, *, 0)为BCI-代数.本文通过在X中引入二元运算“·”x·y=(0*(0*x))*(0*y):(0*y),(x, y∈X),证明了x·y=inf{z∈X|z*x≤y, x, y∈X}及(X,·)为可换幂幺半群.从而揭示了BCI-代数内在的半群结构.
In this paper, we introduce a binary operation '·' on a BCI-algebra (X, * ,0) as: x · y = (0 * (0 * x)) * (0 * y), (for any x,y ∈ X), and prove x · y = inf{z ∈ X|z*x<y} and that (X,·) is a commutative unipotent semigroup. Therefore the implied semigroup structure of BCI-algebras is exposed.
