Ideals of Tambara functors

TL;DR

This paper develops an ideal theory for Tambara functors, which are algebraic structures associated with finite groups, extending the classical ideal theory of commutative rings to a $G$-bivariant setting.

Contribution

It introduces a novel ideal theory framework for Tambara functors, providing a new perspective on their algebraic structure in the context of finite groups.

Findings

Formulation of a $G$-bivariant ideal theory for Tambara functors

Extension of classical ideal concepts to Tambara functors

Potential applications to equivariant algebraic structures

Abstract

For a finite group $G$, a Tambara functor on $G$ is regarded as a $G$-bivariant analog of a commutative ring. In this article, we consider a $G$-bivariant analog of the ideal theory for Tambara functors.