# Rectangular bands

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### Definition

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

### Definition

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

### Morphisms

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

### Properties

 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]?:

### Subclasses

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

### Superclasses

Normal bands

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