Description Usage Arguments Details Value Note Author(s) References See Also Examples

Find the congruence relations of a given abstract or a partially ordered semigroup.

1 |

`S` |
an object from the ' |

`PO` |
(optional) the partial order table |

`uniq` |
(optional and logical) whether or not return the unique congruence relations |

Congruencies are equivalence relations that preserve the operation between the correspondent classes in the algebraic structure. In this case, the different congruence classes are based on the substitution property of the semigroup object.

An object of '`Congruence`

' class.
The items included are:

`S` |
semigroup of relations |

`PO` |
partial order table (if specified) |

`clu` |
congruence classes |

If the partial order is supplied in the input, then the computation of the congruence classes is slightly faster than for an abstract semigroup.

Antonio Rivero Ostoic

Hartmanis, J. and R.E. Stearns *Algebraic Structure Theory of Sequential Machines*. Prentice-Hall. 1966.

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