B-algebra


Definition

(I)\(\forall x : x * x = 0\)
(II)\(\forall x : x * 0 = x\)
(III)\(\forall x,y,z \in X : (x * y) * z = x * (z * (0 * y))\)
THEOREM    \(\forall y,z \in X : y * z = y * (0 * (0 * z))\)

Proof available

THEOREM   

\(\circ\) is left-cancellable.

Proof available

THEOREM   

\(\circ\) is right-cancellable.

Proof available

See also

Proper supersets