A partial order can then be defined as x ≤ y iff x * y = 0. A BCK-algebra is said to be bounded if it has a largest element, usually denoted by 1. In a bounded commutative BCK-algebra the least upper bound of two elements x ∨ y = 1 * ((1 * x) ∧ (1 * y)), which makes it a distributive lattice. ==Examples== Every abelian group is a BCI-algebra...

Found on http://en.wikipedia.org/wiki/BCK_algebra

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