1974/11/01 by Edward Formanek, Arun Vinayak Jategaonkar · 1 citation
Mathematics · Chemistry · #Rings, Modules, and Algebras #Commutative Algebra and Its Applications #Algebraic structures and combinatorial models #Noetherian #Subring #Mathematics #Pure mathematics #Finitely-generated abelian group #Ring (chemistry) #Noetherian ring #Commutative property #Discrete mathematics #Artinian ring #Algebra over a field #Chemistry
paper · doi:10.2307/2039890
openalex publication_date 1974/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Let S be a subring of a ring R such that R is a finitely generated right S-module. Clearly, if S is a right Noetherian ring then so is R. Generalizing a result of P. M. Eakin, we show that if R is right Noetherian and S is commutative then S is Noetherian. We also show that if RS has a finite generating set \ u1, ⋯ ,um\ such that uiS = Sui for 1 ≤ i ≤ m, then a right R-module is Noetherian, Artinian or semisimple iff it is respectively so as a right S-module. This yields a result of Clifford on group algebras.