# Differences

This shows you the differences between two versions of the page.

m-zeroid [2016/11/21 10:42] jipsen |
m-zeroid [2016/11/21 11:09] (current) jipsen |
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====Basic results==== | ====Basic results==== | ||

+ | All subdirectly irreducible algebras are linearly ordered. | ||

+ | |||

+ | The lattice is always bounded, with top element $0$. | ||

+ | |||

+ | The bottom element $-0$ is the identity of $+$. | ||

+ | |||

+ | The dual operation $x\cdot y=-(-y+-x)$ is the fusion of a commutative integral involutive semilinear residuated lattice. In fact, m-zeroids are precisely the duals of these residuated lattices, which are also known as involutive IMTL algebras. | ||

====Properties==== | ====Properties==== | ||

Line 65: | Line 72: | ||

====Subclasses==== | ====Subclasses==== | ||

- | [[]] | + | [[TBD]] |

====Superclasses==== | ====Superclasses==== | ||

- | [[]] | + | [[TBD]] |

- | | + | |

- | [[]] | + | |

- | | + | |

- | [[]] | + | |

====References==== | ====References==== | ||

- | [(PG1994> | ||

J. B. Palmatier and F. Guzman, | J. B. Palmatier and F. Guzman, | ||

\emph{M-zeroids structure and categorical equivalence}, | \emph{M-zeroids structure and categorical equivalence}, | ||

Studia Logica, | Studia Logica, | ||

- | \textbf{100}(5) 2012, 975--1000)] | + | \textbf{100}(5) 2012, 975--1000 |

- | | + | |

- | [(COM2000> | + | |

- | Roberto L. O. Cignoli, Itala M. L. D'Ottaviano, Daniele Mundici, | + | |

- | \emph{Algebraic foundations of many-valued reasoning}, | + | |

- | Trends in Logic---Studia Logica Library | + | |

- | \textbf{7} Kluwer Academic Publishers | + | |

- | 2000, x+231)] | + | |

- | | + | |

- | [(Mu1987> | + | |

- | Daniele Mundici, | + | |

- | \emph{Bounded commutative BCK-algebras have the amalgamation property}, | + | |

- | Math. Japon., | + | |

- | \textbf{32} 1987, 279--282)] | + |

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