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