Semi--vector spaces and units of measurement

Abstract

This paper is aimed at introducing an algebraic model for physical scales and units of measurement. This goal is achieved by means of the concept of ``positive space'' and its rational powers. Positive spaces are 1-dimensional ``semi-vector spaces'' without the zero vector. A direct approach to this subject might be sufficient. On the other hand, a broader mathematical understanding requires the notions of sesqui- and semi-tensor products between semi-vector spaces and vector spaces. So, the paper is devoted to an original contribution to the algebraic theory of semi-vector spaces, to the algebraic analysis of positive spaces and, eventually, to the algebraic model of physical scales and units of measurement in terms of positive spaces.