Boolean algebras with operators

http://math.chapman.edu/cgi-bin/structures.pl?Boolean_algebras_with_operators より：

Abbreviation: BAO

Definition: A Boolean algebra with operators is a structure A = (A,∨,0, ∧,1,¬,f_i (i ∈ I)) such that

1. (A,∨,0,∧,1,¬) is a Boolean algebra,
2. f_i is join-preserving in each argument: f_i( ..., x∨y, ...) = f_i(..., x, ...)∨f_i(..., y, ...), and
3. f_i is normal in each argument: f_i(..., 0, ...) = 0 for each i ∈ I.

Morphisms: Let A and B be Boolean algebras with operators of the same signature. A morphism from A to B is a function h : A→B that is a Boolean homomorphism and preserves all the operators: h(f_i(x₁, ..., x_n)) = f_i(h(x₁), ..., h(x_n)).