An application of two-edge coloured graphs to group algebras of non-noetherian groups (Developments of Language, Logic, Algebraic system and Computer Science)

Abstract

In this note, we introruce an SR-graph and an SR-cycle; we show that certain SR-graphs have SR-cycles. The class of SR-graphs is a subclass of the class of two-edge coloured graphs in which an SR-cycle is called an alternating cycle. We also consider an application of SR-graphs to group algebras; how to prove primitivity of group algebras of non-noetherian groups.