I would like to see explicit computations of the Burnside ring $A(G)$ when $G$ is a small Abelian group, such as $G=\mathbb{Z}/2,\mathbb{Z}/2^n,\mathbb{Z}/p^n$ where $p$ is an odd prime and $n\geqslant 1$. Here, by explicit I mean in terms of generators and relations. I know that there there is a certain map with finite cokernel. But, I don't see any generators in these descriptions. Surely, for something like $\mathbb{Z}/2$ it must be well known!

I would be very grateful for any reference. Here, $\mathbb{Z}/k$ is the cyclic group of order $k$.

I particular, I wonder if there is a ``canonical'' presentation of this ring?!?

I would be very grateful for any references.