2010/03/10 by Tyler Foster, Foster, Tyler
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.1003.2081
7 pages
arxiv created 2010/03/10 · openalex publication_date 2010/03/10 · arxiv updated 2010/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note, we construct and study an algebraic system similar to the natural numbers, but with noncommutative addition. The addition we introduce is a binary operation that commutes with itself in the sense of N. Durov. Neverheless, the multiplication in this system (defined by iterating the noncommutative addition) turns out to be associative, commutative, and distributive over addition, and the resulting system has interesting and nontrivial arithmetic.