2007/10/05 by Josef Janyška, Janyška, Josef, Marco Modugno +3 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #12K10 #15A69 #16Y60 #70Sxx #Commutative Algebra (math.AC) #Digital Image Processing Techniques #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AC #math.MP #msc:12K10 #msc:15A69 #msc:16Y60 #msc:70Sxx
paper · pdf · doi:10.48550/arxiv.0710.1313
28 pages, LaTeX with custom styles included in the source file
arxiv created 2007/10/05 · openalex publication_date 2007/10/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
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.