2012/06/29 by Géza Kós, Kós, Géza
Computer Science · Mathematics · #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.AC #math.RA
paper · pdf · doi:10.48550/arxiv.1206.7005
arxiv created 2012/06/29 · openalex publication_date 2012/06/29 · arxiv updated 2012/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we prove the following fact: if finite many elements p1,p2,...,pn of a unique factorization domain are given such that the greatest common divisor of each pair (pi,pj) can be expressed as a linear combination of pi and pj then the greatest common divisor of all pis also can be expressed as a linear combination of p1,...,pn. We prove am analogous statement in commutative rings.