# Differences

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unary_algebras [2012/07/08 23:33] jipsen |
unary_algebras [2012/07/08 23:34] (current) jipsen |
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====Examples==== | ====Examples==== | ||

- | Example 1: The free unary algebra on one generator is isomorphic to $I^*$, the set of all $n$-tuples of I for $n\in\omega$. The empty tuple is the generator $x$, and the operations $f_i$ are defined by $f_i((i_1,\ldots,i_n))=(i,i_1,\ldots,i_n)$. | + | Example 1: The free unary algebra on one generator is isomorphic to $I^*$, the set of all $n$-tuples of $I$ for $n\in\omega$. The empty tuple is the generator $x$, and the operations $f_i$ are defined by $f_i((i_1,\ldots,i_n))=(i,i_1,\ldots,i_n)$. |

The free unary algebra on $X$ generators is a union of $|X|$ disjoint copies of the one-generated free algebra. | The free unary algebra on $X$ generators is a union of $|X|$ disjoint copies of the one-generated free algebra. | ||

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

- | [[Permutation unary algebras]] subvariety | + | [[Permutation unary algebras]] subvariety |

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

- | [[Duo-unary algebras]] subreduct | + | [[Duo-unary algebras]] subreduct |

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