Let $U\subset{{\bf R}}^{n}$ be an open subset of the standard vector space ${{\bf R}}^{n}$. We define ${\cal O}_{{{\bf R}}^{n}}(U)$ as the vector space over ${{\bf C}}_{\varepsilon}$ consisting of formal Laurent series

$$f=\sum_{k_{1},...,k_{n}\in{{\bf Z}}^{n}}a_{k_{1}...k_{n}}z_{1}^{k_{1}}...z_{n}^{k_{n}},$$

where $z_{1},...,z_{n}$ are formal variables, $a_{k_{1}...k_{n}}\in{{\bf C}}_{\varepsilon}$, and for any $(y_{1},...,y_{n})\in U$ we have: $lim_{\sum_{i}|k_{i}|\to\infty}(v(a_{k_{1}...k_{n}})+\sum_{i}k_{i}y_{i})=+\infty$.