Fatelo, J. P.Martins-Ferreira, Nelson2019-02-192019-02-192019-01-201532-4125http://hdl.handle.net/10400.8/3838This work is supported by Fundação para a Ciência e a Tecnologia (FCT) and Centro2020 through the Project references: UID/Multi/04044/2013 and PAMI – ROTEIRO/0328/2013 (No 022158) and also by CDRSP and ESTG from the Polytechnic Institute of Leiria.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.enggeodesic pathternary operationunit intervalunitary ringsmidpoint algebrasinvolutive medial monoidMobi algebrajournal articlehttps://doi.org/10.1080/00927872.2018.1501575