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Unary Algebras

Abbreviation: Unar

Definition

A \emph{unary algebra} is a structure A=A,(fi:∈I) of type 1:iI such that fi is a unary operation on A for all iI.

Morphisms

Let A and B be unary algebras over the same index set I. A morphism from A to B is a function h:AB that is a homomorphism: h(fi(x))=fi(h(x)) for all iI.

Examples

Example 1: The free unary algebra on one generator is isomorphic to I, the set of all n-tuples of I for nω. The empty tuple is the generator x, and the operations fi are defined by fi((i1,,in))=(i,i1,,in).

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

Basic results

Properties

Finite members

Depends on I

Subclasses

Superclasses

Duo-unary algebras subreduct

References


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