### On the structure theory of graded Burnside rings

#### Abstract

Let $G$ denote a finite group and let $S$ be a finite $G$-set. It is well known that the Burnside ring $\Omega(G)$ of $G$ has its elements as the formal differences of isomorphism classes of finite G-sets. In \cite{Nw}, the category $(G, S, \Omega(G))$-gr, which consists of $\Omega(G)$-modules graded by $S$ as objects and the degree preserving $\Omega(G)$-linear maps as morphisms, was introduced. Using this category as a springboard, some interesting results in the structure theory of graded Burnside rings are brandished.

**Published:**2013-03-09

**How to Cite this Article:**Kenneth K. Nwabueze, On the structure theory of graded Burnside rings, Algebra Letters, Vol 2013 (2013), Article ID 1 Copyright © 2013 Kenneth K. Nwabueze. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Algebra Letters

ISSN 2051-5502

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