Geometry of Autometrized Lattice Ordered Monoids
arXiv:2402.01907
Abstract
In this paper, we study the geometry of AL-monoids by introducing the concept of metric betweeness and its properties t1, t2,, B-linearity, D-linearity, lattice betweeness, B-linearity, and Dlinearity, segments and equilateral triangles. It is proved that there do not exist equilateral triangles in AL-monoids. It is also proved that any AL-monoid is ptolemaic.
arXiv comment9 pages. arXiv admin note: text overlap with arXiv:2402.00361