2013/10/25 by Bernard Le Stum, Stum, Bernard Le, Adolfo Quirós +1
Computer Science · Mathematics · #Commutative Algebra and Its Applications #FOS: Mathematics #Quantum Algebra (math.QA) #Quantum Computing Algorithms and Architecture #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.QA #math.RA
paper · pdf · doi:10.48550/arxiv.1310.8143
2013 - 87
arxiv created 2013/10/25 · openalex publication_date 2013/10/25 · arxiv updated 2013/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the notions of quantum characteristic and quantum flatness for arbitrary rings. More generally, we develop the theory of quantum integers in a ring and show that the hypothesis of quantum flatness together with positive quantum characteristic generalizes the usual notion of prime positive characteristic. We also explain how one can define quantum rational numbers in a ring and introduce the notion of twisted powers. These results play an important role in many different areas of mathematics and will also be quite useful in a subsequent work of the authors.