1-) If y, z ∈ Z with gcd(y, z) = 0, then y = 0 and z = 0.
2-) If y, z ∈ Z with gcd(y, z) = −z, then y divides z and n < 0.
3-) For any y, z ∈ Z, gcd(y, z) = gcd(z, y).
4-) If L is a distributive lattice and y ∈ L, and if w and q are complements of y, then w = q.
5-) B is a Boolean ring. For any y ∈ Y and any k ≥ 2, y^k = y.