Idempotent means on free binary systems do not exist
Justin Tatch Moore
TL;DR
This paper proves that free binary systems cannot have idempotent means, refuting a previous conjecture, and demonstrates that an extended version of Hindman's theorem for nonassociative systems is false.
Contribution
The paper establishes the nonexistence of idempotent means in free binary systems and disproves a conjectured extension of Hindman's theorem to nonassociative systems.
Findings
Free binary systems do not admit idempotent means
The conjectured extension of Hindman's theorem is false in nonassociative systems
Refutes the author's previous conjecture on idempotent means
Abstract
Free binary systems are shown to not admit idempotent means. This refutes a conjecture of the author. It is also shown that the extension of Hindman's theorem to nonassociative binary systems formulated and conjectured by the author is false.
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Taxonomy
Topicsadvanced mathematical theories · Functional Equations Stability Results · Advanced Topology and Set Theory