A sequential algebra is a structure A = (A,∨,0, ∧,1,¬,o,e,▷,◁) such that
∧,1,¬) is a Boolean algebra,
(A,o,e) is a monoid,
▷ is the right-conjugate of o: (xoy)∧z = 0 ⇔ (x▷z)∧y = 0
◁ is the left-conjugate of o: (xoy)∧z = 0 ⇔ (z◁y)∧x = 0
▷,◁ are balanced: x▷e = e◁x
o is euclidean: x·(y◁z) ≤ (x·y)◁z.
Let A and B be sequential 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▷y) = h(x)▷h(y) and h(x◁y) = h(x)◁h(y) and h(e) = e.
|Congruence n-permutable||yes, n = 2|
|Congruence extension property||yes|
|Definable principal congruences||yes|
|Equationally definable principal congruences||yes|
|Strong amalgamation property||no|
|Epimorphisms are surjective||no|