Is there a name for a set together with a unary operation?
If so, where can I learn more about them? Is there anything interesting about them? Are they simply a special case of groups? It simply occurred to me and Googling around has failed me.
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7It is called a function from the set to itself.... – N. S. Apr 01 '12 at 00:17
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You might also be interested in involutions. They tend to appear in all sorts of algebraic situations. See also here. – Dejan Govc Apr 01 '12 at 00:21
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1From Wikipedia/Outline of algebraic structures#Simple structures: "Unary system: S and a single unary operation over S." – Apr 01 '12 at 01:24
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2I think some people define discrete dynamical systems that way. – Michael Greinecker Apr 01 '12 at 02:20
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Maybe just an endomorphism? – Sambo Jun 28 '23 at 01:04
3 Answers
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They are called monounary algebras for example in this paper:
https://www.researchgate.net/publication/225623822_Monounary_algebras
bof
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I have seen the term "unoid" - a set with several unary operations - in the book "Algebraic Systems" by A.I. Mal'cev. So "1-unoid" can be an answer.
The theory of 1-unoids is not entirely devoid. For example, it contains the Recursion Theorem: https://proofwiki.org/wiki/Principle_of_Recursive_Definition
Victor M
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