1951/10/01 by Tadasi Nakayama · 6 citations
Mathematics · #Rings, Modules, and Algebras #Commutative Algebra and Its Applications #Advanced Topics in Algebra #Mathematics #Finitely-generated abelian group #Ideal (ethics) #Ring (chemistry) #Pure mathematics #Combinatorics #Maximal ideal #Discrete mathematics #Law
paper · pdf · doi:10.1017/s0027763000012265
published in Nagoya Mathematical Journal 3, 139-140 (Cambridge University Press)
openalex publication_date 1951/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Theorem 5 of Azumaya’s recent article can be formulated in the following generalized form: Let R be a ring. Let m be a finitely generated right-module of R such that m R = m. Assume that m = u 1 r + u b r + … + u m r for every generating system of u 1 , u 2 , …, u m of m and for every maximal right-ideal r of R . Then m = 0.