Torsion-free Abelian Groups, Valuations and Twisted Group Rings

1988/06/01 by Gervasio G. Bastos, T. Viswanathan · 1 voice
Mathematics · Chemistry · #Rings, Modules, and Algebras #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Mathematics #Abelian group #Monoid #Pure mathematics #Residue field #Torsion (gastropod) #Commutative property #Residue (chemistry) #Group ring #Group (periodic table) #Field (mathematics) #Chemistry

paper · pdf · doi:10.4153/cmb-1988-021-x

openalex publication_date 1988/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Abstract Anderson and Ohm have introduced valuations of monoid rings k [Γ] where k is a field and Γ a cancellative torsion-free commutative monoid. We study the residue class fields in question and solve a problem concerning the pure transcendence of the residue fields.

Discussions

• $\newcommand{\Q}{\mathbb{Q}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\N}{\mathbb{N}} \newcommand{\R}{\mathbb{R}} \DeclareMathOperator{\Frac}{Frac} \DeclareMathOperator{\trdeg}{trdeg} \newcommand{\U}{\ [stackexchange, 6 points]