Lambda-conductors for group rings

TL;DR

This paper explores the lambda-ring concept of conductor ideals in group rings of finite abelian groups, showing that for primary groups, the lambda-conductor equals the intersection of the classical conductor and augmentation ideal.

Contribution

It introduces the lambda-conductor for group rings and characterizes it for primary groups, linking it to classical concepts.

Findings

Lambda-conductor defined for group rings.

For primary groups, lambda-conductor equals the intersection of classical conductor and augmentation ideal.

Provides a new perspective on conductor ideals in lambda-ring context.

Abstract

This paper discusses the lambda-ring version of the notion of conductor ideal for the group ring of a finite abelian group. We prove that if the group is primary, the lambda-conductor is the intersection of the classical conductor and the augmentation ideal.