The Spectrum of the Burnside Tambara Functor of a Cyclic Group

TL;DR

This paper characterizes the prime ideals of the Burnside Tambara functor for cyclic groups, providing a complete description of its prime spectrum and partial results for broader classes of groups.

Contribution

It fully describes the prime spectrum of the Burnside Tambara functor for cyclic groups, advancing understanding of its algebraic structure.

Findings

Complete prime spectrum for cyclic groups

Family of prime ideals derived for Burnside Tambara functor

Partial results for non-cyclic groups

Abstract

We derive a family of prime ideals of the Burnside Tambara functor for a finite group $G$. In the case of cyclic groups, this family comprises the entire prime spectrum. We include some partial results towards the same result for a larger class of groups.