A nonassociative relation algebra is a structure A = (A,∨,0, ∧,1,¬,o,∪,e) such that
∧,1,¬) is a Boolean algebra,
e is an identity for o: xoe = x and eox = x,
o is join-preserving: (x∨y)oz = (xoz)∨(yoz)
∪ is an involution: x∪∪ = x and (xoy)∪ z = y∪ox∪
∪ is join-preserving: (x∨y)∪ z = x∪∨y∪
o is residuated: x∪o(¬(xoy)) ≤ ¬y.
Let A and B be relation algebras. A morphism from A to B is a function h : A → B that is a Boolean homomorphism and preserves o, ∪, e: h(xoy) = h(x)oh(y) and h(x∪) = h(x)∪ and h(e) = e.
|Congruence n-permutable||yes, n = 2|
|Congruence extension property||yes|
|Definable principal congruences|
|Equationally definable principal congruences|
|Strong amalgamation property|
|Epimorphisms are surjective|