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We begin by introducing an algebraic structure with three constants and oneternary operation to which we call mobi algebra. This structure has beendesigned to capture the most relevant properties of the unit interval that areneeded in the study of geodesic paths. Another algebraic structure, calledinvolutive medial monoid (IMM), can be derived from a mobi algebra. We proveseveral results on the interplay between mobi algebras, IMM algebras andunitary rings. It turns out that every unitary ring with one half uniquelydetermines and is uniquely determined by a mobi algebra with one double. Thispaper is the second of a planned series of papers dedicated to the study ofgeodesic paths from an algebraic point of view.

Mobi algebra as an abstraction to the unit interval and its comparison to rings