A *sequential algebra* is a structure ** A** = (

(*A*,∨,0,
∧,1,¬) is a Boolean algebra,

(*A*,o,*e*) is a monoid,

▷ is the *right-conjugate* of o:
(*x*o*y*)∧*z* = 0 ⇔ (*x*▷*z*)∧*y* = 0

◁ is the *left-conjugate* of o:
(*x*o*y*)∧*z* = 0 ⇔ (*z*◁*y*)∧*x* = 0

▷,◁ are *balanced*:
*x*▷*e* = *e*◁*x*

o is *euclidean*:
*x*·(*y*◁*z*) ≤ (*x*·*y*)◁*z*.

**Remark**:

Let ** A** and

Classtype | variety |

Equational theory | undecidable |

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 | yes |

Congruence uniform | yes |

Congruence extension property | yes |

Definable principal congruences | yes |

Equationally definable principal congruences | yes |

[Discriminator variety]? | no |

Amalgamation property | no |

Strong amalgamation property | no |

Epimorphisms are surjective | no |

[Size 2]?:

[Size 3]?:

[Size 4]?:

[Size 5]?:

[Size 6]?:

[Representable sequential algebras]?

[Semiassociative sequential algebras]?