A *commutative residuated lattice* is a residuated lattice ** L** = (

· is commutative: *x**y* = *y**x*.

**Remark**:

Let ** L** and

Classtype | Variety |

Equational theory | Decidable |

Quasiequational theory | Undecidable |

First-order theory | Undecidable |

Locally finite | No |

Residual size | Unbounded |

Congruence distributive | Yes |

Congruence modular | Yes |

Congruence n-permutable | Yes, n=2 |

Congruence regular | No |

Congruence e-regular | Yes |

Congruence uniform | No |

Congruence extension property | Yes |

Definable principal congruences | No |

Equationally definable principal congruences | No |

Amalgamation property | |

Strong amalgamation property | |

Epimorphisms are surjective |

[Size 2]?: 1

[Size 3]?: 3

[Size 4]?: 16

[Size 5]?: 100

[Size 6]?: 794

FLe-algebras

[Commutative residuated join-semilattices]?

[Commutative residuated meet-semilattices]?

Residuated lattices