Simplicial Burnside ring

TL;DR

This paper explores the mathematical structure of the simplicial Burnside ring, connecting it with the slice Burnside ring to better understand ghost maps, idempotents, and prime spectra within these algebraic objects.

Contribution

It introduces new links between the Burnside ring and the slice Burnside ring, enhancing understanding of their algebraic properties and spectral characteristics.

Findings

Established connections between Burnside and slice Burnside rings

Analyzed ghost maps and idempotents in these rings

Explored prime spectrum structure of the rings

Abstract

This paper develops links between the Burnside ring of a finite group $G$ and the slice Burnside ring}. The goal is to gain a better understanding of ghost maps, idempotents, prime spectrum of these Burnside rings and connections between them.