Rectangular bands

A rectangular band is a band B = (B,·) such that · is rectangular: x·y·x = x.

A rectangular band is a band B = (B,·) such that x·y·z = x·z.

Let B and C be rectangular bands. A morphism from B to C is a function h : B→C that is a homomorphism: h(xy) = h(x)h(y).

Classtype	variety
Equational theory	decidable in polynomial time
Quasiequational theory
First-order theory
Locally finite	yes
Residual size
Congruence distributive
Congruence modular
Congruence n-permutable
Congruence regular
Congruence uniform
Congruence extension property
Definable principal congruences
Equationally definable principal congruences
Amalgamation property
Strong amalgamation property
Epimorphisms are surjective

[Size 1]?: 1
[Size 2]?:
[Size 3]?:
[Size 4]?:
[Size 5]?:
[Size 6]?:
[Size 7]?:

[Left-zero semigroups]?
[Right-zero semigroups]?