A Boolean module over a relation algebra R is a structure A = (A,∨,0, ∧,1,¬,fr (r ∈ R)) such that
∧,1,¬) is a Boolean algebra,
fr is join-preserving: fr(x∨y) = fr(x)∨fr(y)
fr is normal: fr(0) = 0
f1' is the identity map: f1'(x) = x
fr(fs(x)) = fros(x).
Let A and B be Boolean modules over a realtion algebra. A morphism from A to B is a function h : A→B that is a Boolean homomorphism and preserves all fr: h(fr(x)) = fr(h(x)).
|Congruence n-permutable||yes, n = 2|
|Congruence extension property||yes|
|Definable principal congruences||no|
|Equationally definable principal congruences||no|
|Strong amalgamation property|
|Epimorphisms are surjective|