∈ d-1 (0). Since d(xy) = xd(y) ∧ d(x)y = x0 ∧ 0y =
x ∧ 0 = 0, we get xy ∈ d-1 (0). Hence d-1 (0) is a
BCC-subalgebra of G. #
Note that d-1 (0) is, in general, not an
ideal of G, as seen in the previous example, (23)1
∈ d-1 (0) and 3 ∈ d-1 (0) but 21 ∉ d-1 (0).