Abstract / Synopsis
A binary operation # on Z+ is said to be an associative arithmetic if both # and its iteration — the binary operation ∗ defined recursively by: x∗1 = x and x∗y = [x ∗ (y − 1)]#x — are associative. E. Rosinger [6] showed that under reasonable conditions an associative arithmetic must be ordinary addition. However, in the general case, there are associative arithmetics that are not ordinary addition. This paper gives examples of these as well as results towards a structure theorem for associative arithmetics. The paper also describes the role that this particular math problem has played in my mathematical life.
DOI
10.5642/jhummath.JDEM9972
Recommended Citation
Marion D. Cohen, "My Own Private World of Non-Ordinary Associative Arithmetics," Journal of Humanistic Mathematics, Volume 14 Issue 2 (July 2024), pages 60-106. DOI: 10.5642/jhummath.JDEM9972. Available at: https://scholarship.claremont.edu/jhm/vol14/iss2/5
