Author(s): Fatelo, J. P. ; Martins-Ferreira, Nelson
Date: 2019
Persistent ID: http://hdl.handle.net/10400.8/3838
Origin: IC-online
Project/scholarship: info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID/Multi/04044/2013/PT;
Subject(s): geodesic path; ternary operation; unit interval; unitary rings; midpoint algebras; involutive medial monoid; Mobi algebra
We introduce a new algebraic structure, called mobi algebra, consisting of three constants and one ternary operation. The canonical example of a mobi algebra is the unit interval with the three constants 0, 1, and 1/2 and the ternary operation given by the formula x−yx+yz. We study some of its properties and prove that every unitary ring with one half uniquely determines and is uniquely determined by a mobi algebra with one double. Another algebraic structure, called involutive medial monoid (IMM), is considered to establish the passage between rings and mobi algebras.
