In this paper, we investigate ideals and idempotents of a ring of generalized power series. We show that: $[[(R\anpha)^{s,.}]] = [[R^{s,.}]].C_{\anpha}$ and $[[(R/I)^{S,.}]]\cong [[R^{S,.}]]/[[I^{S,.}]]$, and discuss the relation between $[[sqrt{I}^{S,.}]]$ and $sqrt{[[I^{S,.}]]}$. We also characterize the idempotents of a ring of generalized power series.