# Differences

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

distributive_lattice_ordered_semigroups [2018/10/14 15:55] jipsen |
distributive_lattice_ordered_semigroups [2018/10/14 16:16] (current) jipsen |
||
---|---|---|---|

Line 21: | Line 21: | ||

Example 1: Any collection $\mathbf A$ of binary relations on a set $X$ such that $\mathbf A$ is closed under union, intersection and composition. | Example 1: Any collection $\mathbf A$ of binary relations on a set $X$ such that $\mathbf A$ is closed under union, intersection and composition. | ||

- | Andreka 1991 AU proves that these examples generate the variety DLOS. | + | H. Andreka[(Andreka1991)] proves that these examples generate the variety DLOS. |

====Basic results==== | ====Basic results==== | ||

Line 51: | Line 51: | ||

$\begin{array}{lr} | $\begin{array}{lr} | ||

f(1)= &1\\ | f(1)= &1\\ | ||

- | f(2)= &\\ | + | f(2)= &6\\ |

- | f(3)= &\\ | + | f(3)= &44\\ |

- | f(4)= &\\ | + | f(4)= &479\\ |

f(5)= &\\ | f(5)= &\\ | ||

- | \end{array}$ | ||

- | $\begin{array}{lr} | ||

- | f(6)= &\\ | ||

- | f(7)= &\\ | ||

- | f(8)= &\\ | ||

- | f(9)= &\\ | ||

- | f(10)= &\\ | ||

\end{array}$ | \end{array}$ | ||

- | |||

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

- | [[...]] subvariety | + | [[Distributive lattice-ordered monoids]] |

- | | + | |

- | [[...]] expansion | + | |

+ | [[Commutative distributive lattice-ordered semigroups]] | ||

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

- | [[...]] supervariety | + | [[Lattice-ordered semigroups]] |

- | | + | |

- | [[...]] subreduct | + | |

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

- | [(Andreka1991> | + | [(Andreka1991>Hajnal Andreka, \emph{Representations of distributive lattice-ordered semigroups with binary relations}, Algebra Universalis \textbf{28} (1991), 12--25)] |

- | Hajnal Andr\'eka, \emph{Representations of distributive lattice-ordered semigroups with binary relations}, Algebra Universalis \textbf{28} (1991), 12--25 | + | |

- | [[MRreview]] | + | |

- | )] | + | |

Trace: