Semiring of formal power series with non-negative coefficients

Question

Has the semiring $\mathbb{Q}_{\geq 0}[[X]]$ of formal power series with non-negative rational coefficients been studied somewhere? For example, I would like to be confirmed that the group of units is $\mathbb{Q}_{>0}$ (this is easy to check). What is the ideal structure? I guess that it is very complicated when compared to the discrete valuation ring $\mathbb{Q}[[X]]$.